Question

A triangle and a parallelogram have the same base and same areas. If the sides of the triangles are $40cm,24cm$ and $32cm$ and the parallelogram stands on the base $40cm.$ Find the height of the parallelogram.

Answer 1

$ar\left(\Delta \right)=\sqrt{s(s-a)(s-b)(s-c)}$

$ar(\parallel gm)=$ base $\times$ height

$\Rightarrow \sqrt{48\left(8\right)\left(16\right)\left(24\right)}=40\times h$

$\Rightarrow h=\frac{16\times 8\times 3}{40}=\frac{48}{5}cm=9.6cm$