Question

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

Answer 1

Step 1

Let the base be$xcm$.

Height$=\frac{1}{3}xcm.$

Step 2

$$\begin{gathered} AreaofParalle\log ram=BaseXHeight \\ Base\times Height=192 \\ x\times \frac{1}{3}x=192 \\ \Rightarrow \frac{1}{3}{x}^2=192 \\ \Rightarrow x^2=192\times 3 \\ \Rightarrow x^2=576 \\ \Rightarrow x=\surd 576 \\ \Rightarrow x=24cm \end{gathered}$$

Base $=x=24cm$

And Height$=\frac{1}{3}x=\frac{1}{3}\times 24$

Height$=8cm$

Hence, Base $=24cm$ and height $=8cm$