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.
(In reply to Geometer's Sketchpad approximation
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