Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 90 yd, find its area.

Explanation:

Step1: Define variables

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

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 4w$ and $P = 90$ into it: $90=2(4w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $2(4w + w)=2\times5w = 10w$. So, $10w=90$.

Step4: Solve for $w$

Divide both sides of the equation $10w = 90$ by 10: $w=\frac{90}{10}=9$ yd.

Step5: Find the length

Since $l = 4w$, then $l=4\times9 = 36$ yd.

Step6: Calculate the area

The area formula of a rectangle is $A=l\times w$. Substitute $l = 36$ and $w = 9$: $A=36\times9=324$ $yd^{2}$.

Answer:

324