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A Triangle in a Square (Posted on 2019-08-21) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Brian Smith    
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Solution Wolfram Alpha exact solution via 5 equations | Comment 2 of 6 |
(In reply to Geometer's Sketchpad approximation by Charlie)

Entering

a+b=e, c+d=e, a^2+e^2=25, b^2+c^2=9, d^2+e^2=16


into Wolfram Alpha, where e is the full side of the square and a, b, c and d are the partial sides, the positive solution is

a = 13/sqrt(17), b = 3/sqrt(17), c = 12/sqrt(17), d = 4/sqrt(17), e = 16/sqrt(17)

The desired area is indeed e^2 = 256/17.

  Posted by Charlie on 2019-08-21 12:25:00
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