Question

The height of a parallelogram is three-eights of its base. If the area of the parallelogram is $96c{m}^2$, find its height and base.

Answer 1

Let $b$ be the base of the parallelogram.

Height of parallelogram $\left(h\right)=\frac{3}{8}b$

Area of parallelogram $=\frac{1}{2}\times b\times h=96{cm}^2\left(\text{Given}\right)$

$\Rightarrow \frac{1}{2}\times b\times \frac{3}{8}b=96$

$\Rightarrow b^2=\frac{96\times 8\times 2}{3}$

$\Rightarrow b=\sqrt{512}=16\sqrt{2}cm$

Therefore,

$h=\frac{3}{8}\times 16\sqrt{2}=6\sqrt{2}cm$