Question

He perimeter of a rectangle is 126 centimeters. What are the dimensions of the sides if the width is seven centimeters shorter than the length?

Answer 1

The width of the rectangle is `28` cm, and the length is `35` cm.

Explanation:

The perimeter of a rectangle is given by the formula:
`P = 2(l + w)`,
where `l` is the length and `w` is the width of the rectangle.

In this problem, the width is explained in terms of the length, so that is how we will express each measurement. We will let
length = `l`
width = `l - 7`

Substituting our expressions for the length & width and `126` for `P`, we can solve the problem.

`126 = 2(l + l - 7)`
`126 = 2(2l - 7)`
`126 = 4l - 14`
`126 + 14 = 4l - 14 + 14`
`140 = 4l`
`140/4 = (4l)/4`
`35 = l`

This tells us that the length of the rectangle is `35` cm. To find the width, we substitute this value in our width expression.

width = `35 - 7 = 28`

So, the width of the rectangle is `28` cm.