Question

the length of a rectangle is 6 yd longer than its width. if the perimeter of the rectangle is 32 yd, find its area.

Explanation:

Step1: Let the width be $x$ yd.

Let the width of the rectangle be $x$ yd. Then the length is $(x + 6)$ yd.

Step2: Use the perimeter formula.

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 32$ yd, we have $32=2((x + 6)+x)$.
Simplify the equation:
\[

$$\begin{align*} 32&=2(2x + 6)\\ 32&=4x+12\\ 4x&=32 - 12\\ 4x&=20\\ x&=5 \end{align*}$$

\]

Step3: Find the length and width.

The width $x = 5$ yd, and the length $x + 6=5 + 6 = 11$ yd.

Step4: Calculate the area.

The area formula of a rectangle is $A=l\times w$. So $A=11\times5 = 55$ square - yards.

Answer:

55 square yards