Question

The height of a parallelogram is one third of its base. If the area of the parallelogram is $192{\text{cm}}^2$, find its height and base.

Answer 1

Let the height of the parallelogram be h cm and base be b cm.

According to the question $h=\frac{1}{3}b$

Area of parallelogram $=$base $\times$ height

$b\times h=192$

$\Rightarrow b\times \frac{1}{3}b=192$

$\Rightarrow b^2=192\times 3$

$\Rightarrow b^2=576$

$\Rightarrow b=\sqrt{576}$

$\Rightarrow b=24cm$

But given $h=\frac{1}{3}b$

$\Rightarrow h=\frac{1}{3}\times 24$

$\Rightarrow h=8cm$

Height of the parallelogram $=h=8cm$

Base $=b=24cm$.