Question

Refer to the isosceles triangle shown, where AB = AC = x. AE is the perpendicular such that AE = p and BC = d. Find the length of CD ___.
(Given that AB$\perp$CD and also, d = 2x)

Answer 1

Area of the triangle $\Delta ABC=\frac{1}{2}\times AE\times BC=\frac{1}{2}\times AB\times CD$
$\Rightarrow$ $AE\times BC=AB\times CD$
$\Rightarrow$ $CD=AE\times \frac{BC}{AB}=\frac{pd}{x},sinced=2x,CD=2p$