Question

The height of a parallelogram is one third of its base. If the area of the parallelogram is $108c{m}^2$, find its base and height.

Answer 1

Area of parallelogram $=base\times height$……….(1)

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

By the given condition,

The height of a parallelogram is one third of its base [Given]

Height of the parallelogram $\left(h\right)$$=\frac{1}{3}\times b$.

Let the base of the parallelogram be $x$.

So, $b=xandh=\frac{1}{3}\times x$.

Area of parallelogram $=108c{m}^2$

Substituting the values of $b$ and $h$ in the formula,

Area of parallelogram $=base\times height$

$108$$=\left(x\right)\times \left(\frac{1}{3}x\right)$

$108=\frac{1}{3}{x}^2$

Multiplying both sides by $3$.

$108\times 3=3\times \frac{1}{3}{x}^2$

So, $x^2=108\times 3$

$x^2=324$

Taking the square root,

$x=\sqrt{324}$

$x=18cm$.

And $h=\frac{1}{3}x=\frac{1}{3}\times 18$

So, $h=6cm$

Hence, the base of the parallelogram is $18cm$ and the height of the parallelogram is $6cm$.