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

Answer:

The width is $24.5in$

Step-by-step 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.

$w=\frac{1}{2}l-8...(2)$

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

$179=2l+2(\frac{1}{2}l-8)$.

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

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

$\Rightarrow 3l=195$

Divide both sides by 3;

$l=65$

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

$w=\frac{1}{2}\times65-8$

$w=32.5-8$

$w=24.5in$