The perimeter of a rectangle is numerically equal to its area. If the width of a rectangle is $\frac{7}{2}\ cm$ then its length is

Given:

The perimeter of a rectangle is numerically equal to its area.

The width of the rectangle is $\frac{7}{2}\ cm$.
To do:

We have to find its length.

Solution:

Let the length of the rectangle be $x$.

This implies,

Perimeter of the rectangle $=2(x+\frac{7}{2})$

Area of the rectangle $=x \times \frac{7}{2}$

According to the question,

$2(x+\frac{7}{2})=x \times \frac{7}{2}$

$2x+7=\frac{7x}{2}$
$2x-\frac{7x}{2}=-7$

$\frac{4x-7x}{2}=-7$

$\frac{-3x}{2}=-7$

$-3x=2(-7)$

$x=\frac{14}{3}$
The length of the rectangle is $\frac{14}{3}\ cm$.