Question

the length of a rectangle is four times its width. if the area of the rectangle is 144 in², find its perimeter.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ inches. Then the length $l = 4w$ inches.

Step2: Use the area formula

The area formula of a rectangle is $A=l\times w$. Substitute $l = 4w$ and $A = 144$ into the formula: $144=4w\times w$. So $144 = 4w^{2}$.

Step3: Solve for $w$

Divide both sides of the equation $144 = 4w^{2}$ by 4: $\frac{144}{4}=w^{2}$, which gives $w^{2}=36$. Taking the square - root of both sides, $w = 6$ (we consider the positive value since width cannot be negative).

Step4: Find the length

Since $l = 4w$, when $w = 6$, then $l=4\times6 = 24$ inches.

Step5: Calculate the perimeter

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 24$ and $w = 6$ into the formula: $P=2(24 + 6)=2\times30=60$ inches.

Answer:

60