Q31. - Geometry

Question

A rectangle having area $392m^2$ is twice as long as it is wide. Find its dimensions.

Step-by-Step Solution

Answer

The dimensions are$28m\times 14m$ .

Step 1. Given information.

Area of the rectangle$A=392m^2$ .

Length is twice as its width.

Step 2. Concept Used.

If b is the width of the rectangle and i is the length of the rectangle.

Then, the area of the rectangle is $A=l\times b$

Step 3. Let’s calculate the dimensions and area of the rectangle.

According to the given situation, length is twice as its width i.e.

$l=2b$

The area of the rectangle;

$\begin{array}{c}A=l\times b\\ 392=\left(2b\right)\times b\\ 392=2b^2\\ b^2=\frac{392}{2}\\ b^2=196\\ b=\sqrt{196}\\ b=14m\end{array}$

Let’s calculate the length of the rectangle.

$\begin{array}{c}l=2\left(14\right)\\ =28m\end{array}$

Therefore, the dimensions of the rectangle is$28m\times 14m$ .