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.

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

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.

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

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.

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

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?