ABCD is a square with points E and F on sides AB and BC respectively. Given DF=4, EF=3, and DE=5 find the area of the square.
Call the side of the square S and angle FDC a.
Then angle DFC=90-a, and since angle DFE=90, angle BFE=a and angle BEF=90-a. So triangles DCF and FBE are similar and S/4=BF/3.
Also BF=S-FC=S-sqrt(16-S^2).
Substitute and solve to find S^2=256/17.
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Posted by xdog
on 2019-08-21 13:29:30 |
solution
