Question

A rectangular yoga mat has a perimeter of 179 inches. The width of the mat is eight less than half the length. Find the width, in inches,of the mat.

Answer 1

The width is
`24.5in`

Explanation:

The perimeter of the rectangular yoga mat can be found using the formula;

`P=2l+2w`.

`\Rightarrow 179=2l+2w...(1)`.

It was given that the width of the mat is eight less than half the length.

`w=(1)/(2)l-8...(2)`

We put equation (2) into equation (1) to get;

`179=2l+2((1)/(2)l-8)`.

`\Rightarrow 179=2l+l-16`.

`\Rightarrow 179+16=2l+l`.

`\Rightarrow 3l=195`

Divide both sides by 3;

`l=65`

We put
`l=65` into equation 2 to get;

`w=(1)/(2)*65-8`

`w=32.5-8`

`w=24.5in`