8/12/2014 ΔCAB is right-angled at A with AC = 8 and AB = 12. Points F, E and D lie on sides AB, BC and CA respectively such that AFED is a rectangle. If AF ≈ x, find an expression for the Area of rectangle AFED in terms of x.

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8/12/2014 Solution. Sketch and label figure to satisfy conditions. If AD ≈ y, then DE ≈ x [since AF = DE].

Using similar triangles, CD/CA = DE/AB so that (8 – y)/8 = x/12.

Simplifying, y = (24 – 2x)/3 (*)

Area of the rectangle, A = xy = (24x – 2x²)/3 [Using (*)]