Problem:
Square EFGH has one vertex on each side of square ABCD. Point E is on AB with AE=7â‹…EB. What is the ratio of the area of EFGH to the area of ABCD?
Answer Choices:
A. 6449​
B. 3225​
C. 87​
D. 852​​
E. 414​​
Solution:
Without loss of generality, assume that F lies on BC and that EB=1. Then AE=7 and AB=8. Because EFGH is a square, BF=AE=7, so the hypotenuse EF of △EBF has length 12+72​=50​. The ratio of the area of EFGH to that of ABCD is therefore
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