# Similar shapes

Please view attachment. Need help with finding value of t.

My working out - note it is wrong
t = (20/44) x 20 = 9.1
I don't understand why we can't do this if the trapezium's are similar shapes.
(edited 9 months ago)
Original post by As.1997
Please view attachment. Need help with finding value of t.

My working out - note it is wrong
t = (20/44) x 20 = 9.1
I don't understand why we can't do this if the trapezium's are similar shapes.

Have you drawn the two shapes youre using the similar argument on and clearly think about the corresponding sides? Deja vu again?
(edited 9 months ago)
A bit of hands-on exploration: You might want to bust out MS Paint (or the Mac equivalent or something, idk), draw a trapezium, and actually enlarge/shrink it (while holding Shift of course to preserve shape), see what similar trapeziums actually look like.

Responding to #4: Better check the third side also is in the right ratio too, just to make sure if your guess on them being similar is correct (it's not)...
(edited 9 months ago)
Original post by mqb2766
Have you drawn the two shapes youre using the similar argument on and clearly think about the corresponding sides? Deja vu again?

This is how I compared the shapes. Not quite sure what I've missed out this time :L
(edited 9 months ago)
Original post by As.1997
This is how I compared the shapes

No. You want to compare the whole trapezium to the bottom one.

The top trapezium is similar to the other two, However, your attempt completely ignores the "heights" so 16 and 4, which is the key part of the question. You want to find the ratio of t to 20 or 44 by finding the scaling factor for a different side.
(edited 9 months ago)
Original post by mqb2766
No. You want to compare the whole trapezium to the bottom one.

The top trapezium is similar to the other two, However, your attempt completely ignores the "heights" so 16 and 4, which is the key part of the question. You want to find the ratio of t to 20 or 44 by finding the scaling factor for a different side.

Good point just saw the 16 and 4 bit which means the 44/20 doesn't make sense.
Original post by mqb2766
No. You want to compare the whole trapezium to the bottom one.

The top trapezium is similar to the other two, However, your attempt completely ignores the "heights" so 16 and 4, which is the key part of the question. You want to find the ratio of t to 20 or 44 by finding the scaling factor for a different side.

I'm looking at the whole trapezium (black triangle) and the bottom one (red triangle).
This would mean t= (16/20)x20 = 16. But this also doesn't add up since the side 44 is being shared between the red and black trapezium.
(edited 9 months ago)
Original post by As.1997
I'm looking at the whole trapezium (black triangle) and the bottom one (red triangle).
This would mean t= (16/20)x20 = 16

Yes. Sounds more sensible, so if the "4" shrunk to zero, then t would be 20 and the scale factor would be 16/16=1. So youre finding t by equating
top side ratio = right side ratio
Original post by mqb2766
Yes. Sounds more sensible, so if the "4" shrunk to zero, then t would be 20 and the scale factor would be 16/16=1. So youre finding t by equating
top side ratio = right side ratio

I'm lost here. Not sure what's going on.
I've been able to get to t=14 using another method. But I can't quite understand why I get different answers and also which one is correct.
Original post by As.1997
I'm lost here. Not sure what's going on.

Think I was a bit garbled-brain not in gear. Taking a step back, trapeziums are similar if they have exactly the same shape, so the sides are all subject to the same scaling factor. Its not just about checking angles which is sufficient for triangles. These 3 trapeziums are not similar in that regard as theyre expanding the height but keeping the base the same.

If you formed a large triangle by putting a cone on the top, and denote the right side by x, then you have using similar triangles with the 20 and 44 bases
(x+4)/20 = (x+20)/44
Then once you have x, you can get t using a simliar argument on the triangle with base t. .

Edit - this is what you did in the previous post and I agree with 14.
(edited 9 months ago)
Original post by mqb2766
Think I was a bit garbled-brain not in gear. Taking a step back, trapeziums are similar if they have exactly the same shapes, so the sides are all subject to the same scaling factor. Its not just about checking angles which is sufficient for triangles. These 3 trapeziums are not similar in that regard as theyre expanding the height but keeping the base the same.

If you formed a large triangle by putting a cone on the top, and denote the right side by x, then you have using similar triangles with the 20 and 44 bases
(x+4)/20 = (x+20)/44
Then once you have x, you can get t using a simliar argument on the triangle with base t. .

Edit - this is what you did in the previous post and I agree with 14.

Thanks a lot
Original post by As.1997
Thanks a lot

To atone for the above, you can do it more simply by considering the change in the horizontal length so for the lower trapezoid, the change is 44-20 = 24 in 16 units along the right, so for the upper trapezoid the change is h - 20 in 4 or
20-h / 4 = 24/16
so
h = 20 - 6 = 14

You could use the large trapezoid as well so
44-h / 20 = 24/16
so
h = 44 - 30 = 14.

Its obv equivalent to sticking the triangle on the top and doing two calcs, but you construct similar triangles in the right part of the trapezoid, so one side the right hand side of the trapezoids, one is part of the base (hence the 20-h or 44-20 or ...) and the third side is paralllel to the left hand side of the trapezoid. connecting the top right vertex of the trapezoid to the base.
(edited 9 months ago)
Original post by mqb2766
To atone for the above, you can do it more simply by considering the change in the horizontal length so for the lower trapezoid, the change is 44-20 = 24 in 16 units along the right, so for the upper trapezoid the change is h - 20 in 4 or
20-h / 4 = 24/16
so
h = 20 - 6 = 14

You could use the large trapezoid as well so
44-h / 20 = 24/16
so
h = 44 - 30 = 14.

Its obv equivalent to sticking the triangle on the top and doing two calcs, but you construct similar triangles in the right part of the trapezoid, so one side the right hand side of the trapezoids, one is part of the base (hence the 20-h or 44-20 or ...) and the third side is paralllel to the left hand side of the trapezoid. connecting the top right vertex of the trapezoid to the base.

I got a little bit lost with this part, "but you construct similar triangles in the right part of the trapezoid". Is the attachment what you meant?

Am I also right to assume that we can use the method you describe because the 4 and the 16 take into consideration that the trapezia are not similar?
(edited 9 months ago)
Original post by As.1997
I got a little bit lost with this part, "but you construct similar triangles in the right part of the trapezoid". Is the attachment what you meant?

Am I also right to assume that we can use the method you describe because the 4 and the 16 take into consideration that the trapezia are not similar?

Not quite. Basically the triangles in the bottom right would be similar to the large triangle constructed above so

The red line(s) are parallel to the left hand side of the trapezoid(s), and teh triangles formed by red line(s), thetrapezpoids right side segment and the trapezoids base segment are all similar (basically the triangle to the right of the appropriate red line). Whats left (to the left of of the triangle) is a parallelogram, so the triangles base line segment is 44-20 or 44-h or 20-h depending on which trapezoid you start with. You can then relate this to the right sides so 16 or 20 or 4.

The triangles are similar to the one constructed above by putting a cone on the top, but as you can map the h directly to the base (parallelogram), you dont need to do two steps.
(edited 9 months ago)