Q16. - Algebra 2

Question

If the perimeter of a rectangle is 12 times the width of the rectangle, then the length of the rectangle is how many times the width?

Step-by-Step Solution

Answer

The length of the rectangle is 5 times the width.

Step 1 – Perimeter of the rectangle.

Suppose $l$ is the length and $w$ is the width of the rectangle.

Then the perimeter$P$ of the rectangle is $P=2\left(l+w\right)$.

Step 2 – Find a mathematical expression for the given situation.

The perimeter of the rectangle is 12 times the width of the rectangle.

This can be mathematically written as follows:

$2\left(l+w\right)=12w$

Step 3 – Find value of l .

Solve $2\left(l+w\right)=12w$:

$\begin{array}{c}2\left(l+w\right)=12w\\ l+w=6w\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}Divide both sides by 2}\\ l=5w\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}Subtract }w\text{ from both sides}\end{array}$

So, the length of the rectangle is 5 times the width.