Question

Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 140.

Answer 1

Given:

Length of the rectangle = $x+4$

Width of the rectangle = $x$

The perimeter of the rectangle is less than 140.

To find:

The inequality for the given situation and solve it.

Solution:

We have,

$l=x+4$

$w=x$

We know that, the perimeter of a rectangle is

$P=2(l+w)$

$P=2(x+4+x)$

$P=2(2x+4)$

$P=4x+8$

It is given that the perimeter of the rectangle is less than 140.

$P$

$4x+8$

$4x$

$4x$

Divide both sides by 4.

$x$

$x$

Therefore, the correct option is A because the sign of inequality is < and the solution of inequality is $x$.