Question

the length of a rectangle is 4 in longer than its width. if the perimeter of the rectangle is 36 in, find its area.

Explanation:

Step1: Define variables

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

Step2: Use the perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 36$ inches, we substitute $l$ and $P$ into the formula: $36=2((w + 4)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $36=2(2w + 4)$. Then distribute the 2: $36 = 4w+8$.

Step4: Solve for $w$

Subtract 8 from both sides: $36-8=4w$, so $28 = 4w$. Divide both sides by 4: $w=\frac{28}{4}=7$ inches.

Step5: Find the length

Since $l=w + 4$, then $l=7 + 4=11$ inches.

Step6: Calculate the area

The area formula of a rectangle is $A=l\times w$. Substitute $l = 11$ and $w = 7$: $A=11\times7 = 77$ square - inches.

Answer:

77