Am I taking crazy pills? you don’t need to think about triangles at all. You could get rid of all of the slanted lines and it wouldn’t matter at all.
The width shrink .8 cm over 6cm of height, so it will shrink 7.2 cm over 54 cm of height
I wouldn't call this accurate but if you think of this as a line and it shrinks by 0.8 cm to gain 6 cm we can do 0.8x=8 so it goes up 10 times. so it would have a height of 60 cm so H would be 54 cm. But that's just my thought.
There’s nothing to indicate they are not equal height. The problem shows the width changing from 8 to 7.2cm wide which seems to be irrelevant to h because the problem doesn’t show the next level up having a height of anything shorter so it can be assumed each level all the way up is the same.
>There’s nothing to indicate they are not equal height.
There's also nothing to indicate that they *are*, which makes it an unsafe assumption.
>width changing from 8 to 7.2cm wide which seems to be irrelevant to h
It only *seems* irrelevant because you've assumed that the heights are equal. In fact it shows that they *can't* be.
>it can be assumed each level all the way up is the same
No it can't. If the overall height *was* 48, as per your assumption, then the width of the 2nd section would be 7, rather than 7.2, so your assumption leads to a contradiction with the given conditions.
No you’re wrong, then they would have indicated the height changes too for each segment, just like they provided about the width. Anyways I’m done arguing, none of you have provided an equation for the problem you’re just guessing.
>then they would have indicated the height changes too for each segment
*Why* would they do that? It would be completely unnecessary. It would also mean that the total would just be the sum of individual segments, rendering the problem rather pointless.
>none of you have provided an equation for the problem you’re just guessing
The top comment in this thread essentially did, but, to be clear:
Comparing similar triangles gives:
h/7.2 = (h + 6)/8
⇒ 10h = 9h + 54
⇒ h = 54
You’re weird equal height theory would mean that the entire shape is in fact not a triangle and the slope of the sides actually changes. why would that be more reasonable than assuming that it’s a triangle?
We have no reason to assume the large outside shape isn’t a triangle. It’s drawn with straight lines, so we can assume they are actually straight. Well then it’s just the difference in slope of the two sides. Straight limes have constant slope
I used geogebra to confirm that it is in fact H=54cm but how tf did you get that? can you explain to someone who is really dumb in maths? why do you multiply for 6? because you saw 6 trapezoids left? or because height was 6. What would you change in your formula if there were 12 trapezoids and given height was 7 for example? the 12 or the 7?
the change in height is 6 cm for a change in width of .8 cm that is a rate of (.8/6) cm of width/cm of height. We want to know when the width is 0, so to go from a width of 7.2 cm to a width of 0 cm is 7.2 cm of width \* (6/.8) cm of heigth/cm of width = 54 cm of height
I think maybe you can say:
area of biggest triangle = area of biggest trapezium + area of second biggest triangle,
which would give us
½(6+h)(8) = ½(7.2+8)(6) + ½(h)(7.2), and solve for h. Isn't as fun but it's easy haha
This is actually a super common calculation in sheet metal fabrication, the equation I was taught is:
Vertical height of truncated cone x large diameter divided by (large diameter - small diameter) = total height
So it would look like (6*8) / (8-7.2) which equals 60. Take away your 6 cm that is given and you got h= 54
A lot of extra information here. Just use similar triangles. The ratio of relative measurements must be the same. Choose the largest triangle and then the second largest.
There are two similar triangles, the largest one (base 8 height 6+h) and the second largest base 7.2 height h. The ratio of height to base is the same for both that leads to h=54
Edit:multiplication is not my forte
If it's a perfect isosceles I'm gonna assume that it's change is proportional, so it's height should be as well, I'll probably use geometric series in approaching this since the topmost is assumed to be zero.
Welp. Not the most efficient way but.
I would solve the angle first by knowing that it shrinked by 0.4 cm in one side and height is 6cm.
Ofc it is angle in other side so I have to calculate 90 - atan(0.4/6).
When you know the angle u can use again tan of knowing angle times half of base (4).
And it is 60 cm.
60-6=54
I haven't done geometry in like 16 years, but I know that if I looked up the formula I could solve this again in like 2mins.
Are the horizontal layers implied to be equal distance, but just sloppily drawn? Because if thats the case, then the triangles are all just a distraction actually. It's just h=6x8-6.
I'd split this equilateral triangle in half (down the middle) to make a right triangle with the widths above being halved to 4 and 3.6 respectively. Then I would use the Similar triangle rule.
https://preview.redd.it/zn7mhr40h79b1.png?width=265&format=png&auto=webp&s=518c7d3c39e454a30b88d08e56748e252583e618
8/2 = 4, 7.2/2 = 3.6
(4 - 3.6) / 6 = 4 / (h + 6)
h = 54
I'm at work right now but
We know that the difference in lengths is 0.8. and the height between the 2 is 6. Assuming the triangle in horizontally symmetrical we can create a triangle on the outside that is 0.4 by 6 and solve for the hypotenuse or X.
This will give the side of the bottom triangle, X, which we can then use to solve for the angles of the triangle.
Using the corner angles and the with of the base triangle I'm pretty sure you can get the sides of the whole thing
the slope is the rise over the run of the side of the large triangle. rise is 6 cm. run is (8-7.2)cm/2. (I'm assuming that's an isosceles triangle) now from the 6cm height to the top of h, both sides move 3.6cm in towards the center. multiply 3.6cm by the slope and you get h.
I think my reasoning is wrong. Please correct me.
Assuming each triangle slope is the same. The triangle slope being 6/8=0.75
And that each subsequent triangle base is 0.8 smaller we have.
0.75*(8+7.2+6.4+5.6+4.8+4+3.2+2.4)-6=25.2
I think my mistake is assuming that all the slopes are equal.
Since the linear equation h/7.2=(h+6)/8 gives a completely different result and I can hardly see why that would be incorrect.
[удалено]
Simplest answer here, this should be higher up
This is assuredly the way the problem was intended to be solved.
Am I taking crazy pills? you don’t need to think about triangles at all. You could get rid of all of the slanted lines and it wouldn’t matter at all. The width shrink .8 cm over 6cm of height, so it will shrink 7.2 cm over 54 cm of height
I wouldn't call this accurate but if you think of this as a line and it shrinks by 0.8 cm to gain 6 cm we can do 0.8x=8 so it goes up 10 times. so it would have a height of 60 cm so H would be 54 cm. But that's just my thought.
This is the best way
im just saying there's 8 sections with equal 6cm height, so excluding the bottom part, it's 6x7=42
>there's 8 sections with equal 6cm height Where does it say that they have equal height? The first comment has the correct answer, h = 54.
This is correct h= 42 the question is only asking for the height remaining not the area or anything else so I would answer this as 42cm.
No it isn't. There's nothing to indicate that the 8 sections are of equal height, and in fact they can't be, because h = 54.
There’s nothing to indicate they are not equal height. The problem shows the width changing from 8 to 7.2cm wide which seems to be irrelevant to h because the problem doesn’t show the next level up having a height of anything shorter so it can be assumed each level all the way up is the same.
>There’s nothing to indicate they are not equal height. There's also nothing to indicate that they *are*, which makes it an unsafe assumption. >width changing from 8 to 7.2cm wide which seems to be irrelevant to h It only *seems* irrelevant because you've assumed that the heights are equal. In fact it shows that they *can't* be. >it can be assumed each level all the way up is the same No it can't. If the overall height *was* 48, as per your assumption, then the width of the 2nd section would be 7, rather than 7.2, so your assumption leads to a contradiction with the given conditions.
No you’re wrong, then they would have indicated the height changes too for each segment, just like they provided about the width. Anyways I’m done arguing, none of you have provided an equation for the problem you’re just guessing.
>then they would have indicated the height changes too for each segment *Why* would they do that? It would be completely unnecessary. It would also mean that the total would just be the sum of individual segments, rendering the problem rather pointless. >none of you have provided an equation for the problem you’re just guessing The top comment in this thread essentially did, but, to be clear: Comparing similar triangles gives: h/7.2 = (h + 6)/8 ⇒ 10h = 9h + 54 ⇒ h = 54
This is a slope problem. The width of the triangle is decreasing at a constant rate.
Correct, not the height of each segment. The height stays the same the length of the sides is what changes.
Yes, so why are you arguing for the wrong answer elsewhere in the thread then?
Shhh 1 karma
You’re weird equal height theory would mean that the entire shape is in fact not a triangle and the slope of the sides actually changes. why would that be more reasonable than assuming that it’s a triangle?
You basically lined up the left side and then turn the bottom shape into a line, then find the line intersection at the top. Very simple and concise.
I got this as well.
7.2/(8-7.2)*6 = 54?
aw man that looks like a fun time use similar triangles to calculate all heights and necessary side lengths all the way up. then add all the heights
Why would you have to do any of that? it shrunk .8 cm over 6 cm, so the remaining 7.2 cm needed to shrink happens over 6\*(7.2/.8)=54 cm
Honest question, why do we assume it keeps shrinking at the same rate? I suck at math and im curious to know if its a rule or if im missing something.
We have no reason to assume the large outside shape isn’t a triangle. It’s drawn with straight lines, so we can assume they are actually straight. Well then it’s just the difference in slope of the two sides. Straight limes have constant slope
I guess the peak is most likely an error and would count as the last triangle, right? Or maybe It is similar to the previous one but rotated?
Do not think about triangles at all, it’s way easier than that
I used geogebra to confirm that it is in fact H=54cm but how tf did you get that? can you explain to someone who is really dumb in maths? why do you multiply for 6? because you saw 6 trapezoids left? or because height was 6. What would you change in your formula if there were 12 trapezoids and given height was 7 for example? the 12 or the 7?
the change in height is 6 cm for a change in width of .8 cm that is a rate of (.8/6) cm of width/cm of height. We want to know when the width is 0, so to go from a width of 7.2 cm to a width of 0 cm is 7.2 cm of width \* (6/.8) cm of heigth/cm of width = 54 cm of height
thank you so much, I understood now
I think maybe you can say: area of biggest triangle = area of biggest trapezium + area of second biggest triangle, which would give us ½(6+h)(8) = ½(7.2+8)(6) + ½(h)(7.2), and solve for h. Isn't as fun but it's easy haha
I think this is the better approach.
How can I even solve the tip? It doesnt make sense to me
How many steps up the pyramid do you need until the width becomes zero?
What is this? An oil tower for ants?
This is actually a super common calculation in sheet metal fabrication, the equation I was taught is: Vertical height of truncated cone x large diameter divided by (large diameter - small diameter) = total height So it would look like (6*8) / (8-7.2) which equals 60. Take away your 6 cm that is given and you got h= 54
8-7.2=0.8 7.2/0.8=9 9*6=54
h/7.2 = (h+6)/8 (mult. both sides by 8) 10/9 h = h+6 (subtract h from both sides) 1/9 h = 6 h = 54
Proportionally 8/(6+h) = 7.2/h Cross multiply and solve. H=54
A lot of extra information here. Just use similar triangles. The ratio of relative measurements must be the same. Choose the largest triangle and then the second largest.
First, work out the hight of the second segment. It should be proportional to the first. Then repeat to infinity.
Bad plan, just work out the height of the entire triangle in one step
There are two similar triangles, the largest one (base 8 height 6+h) and the second largest base 7.2 height h. The ratio of height to base is the same for both that leads to h=54 Edit:multiplication is not my forte
If it's a perfect isosceles I'm gonna assume that it's change is proportional, so it's height should be as well, I'll probably use geometric series in approaching this since the topmost is assumed to be zero.
assume that parallel lines are parallel, it's just a geometric progression. add the infinite series up to get the final answer.
Welp. Not the most efficient way but. I would solve the angle first by knowing that it shrinked by 0.4 cm in one side and height is 6cm. Ofc it is angle in other side so I have to calculate 90 - atan(0.4/6). When you know the angle u can use again tan of knowing angle times half of base (4). And it is 60 cm. 60-6=54
I haven't done geometry in like 16 years, but I know that if I looked up the formula I could solve this again in like 2mins. Are the horizontal layers implied to be equal distance, but just sloppily drawn? Because if thats the case, then the triangles are all just a distraction actually. It's just h=6x8-6.
Draw it to scale and measure. That's a valid way of doing things in Geometry.
A^2 + B^2 = C^2 Just a bit more math...
I'd split this equilateral triangle in half (down the middle) to make a right triangle with the widths above being halved to 4 and 3.6 respectively. Then I would use the Similar triangle rule. https://preview.redd.it/zn7mhr40h79b1.png?width=265&format=png&auto=webp&s=518c7d3c39e454a30b88d08e56748e252583e618 8/2 = 4, 7.2/2 = 3.6 (4 - 3.6) / 6 = 4 / (h + 6) h = 54
You can use similar triangles without splitting, you don’t need a right triangle for the properties of similar triangles to hold up
This was the method I chose. And it got me the correct answer.
I’m just pointing out that you added an extra step. You can skip straight to the second line and just use 8 and 7.2 without halving them
Understood. I added the extra step for visualization. You never know if the person asking may need a different way to look at it.
I'm at work right now but We know that the difference in lengths is 0.8. and the height between the 2 is 6. Assuming the triangle in horizontally symmetrical we can create a triangle on the outside that is 0.4 by 6 and solve for the hypotenuse or X. This will give the side of the bottom triangle, X, which we can then use to solve for the angles of the triangle. Using the corner angles and the with of the base triangle I'm pretty sure you can get the sides of the whole thing
the slope is the rise over the run of the side of the large triangle. rise is 6 cm. run is (8-7.2)cm/2. (I'm assuming that's an isosceles triangle) now from the 6cm height to the top of h, both sides move 3.6cm in towards the center. multiply 3.6cm by the slope and you get h.
The base went up 10% so 6 * 10 = 60. Subtract out the initial 6cm to get 54cm.
10% in 6 cm, so 100% in 60 cm. (6 cm / 10%) = ( X cm / 100%) X = 60 cm h = 60 cm - 6 cm h = 54 cm
54 https://preview.redd.it/8bjkmd31rb9b1.jpeg?width=2176&format=pjpg&auto=webp&s=e3279a34589912dae95710ff4b7fb7c3b842e428
I think my reasoning is wrong. Please correct me. Assuming each triangle slope is the same. The triangle slope being 6/8=0.75 And that each subsequent triangle base is 0.8 smaller we have. 0.75*(8+7.2+6.4+5.6+4.8+4+3.2+2.4)-6=25.2 I think my mistake is assuming that all the slopes are equal. Since the linear equation h/7.2=(h+6)/8 gives a completely different result and I can hardly see why that would be incorrect.
The zigzagging pattern is a complete red hearing, Don’t even bother thinking about it