**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*.

**Scroll
down for the solution.**

**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 – 2*x*)/3
(*)

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