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tino4ka555 [31]
2 years ago
13

Given the isosceles trapezoid below, find AG. Show all the work

Mathematics
1 answer:
Dmitry [639]2 years ago
8 0

We know the width of the rectangle in the middle of the trapezoid is 24 (from the top of the image), so we can subtract that from the bottom width of the trapezoid to get the combined length of the bottom of both triangles.

40 - 24 = 16

Since this is an isosceles trapezoid, both triangle bases are the same length, so we can cut this value in half to get the length of GT and EF

\frac{16}{2} = 8

Finally, we can use the Pythagorean Theorem to find the length of AG:

AG^{2} + GT^{2} = AT^{2}

AG^{2} + 8^{2} = 10^{2}

AG^{2} + 64 = 100

AG^{2} = 36

AG = 6

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