Question

the length of a rectangle is 5 ft longer than its width. if the perimeter of the rectangle is 30 ft, find its area.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ ft. Then the length $l = w + 5$ ft.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 30$ ft, we substitute $l$ and $P$ into the formula: $30=2((w + 5)+w)$.
Simplify the equation:
\[

$$\begin{align*} 30&=2(2w + 5)\\ 30&=4w+10\\ 4w&=30 - 10\\ 4w&=20\\ w&=5 \end{align*}$$

\]

Step3: Find the length

Since $l=w + 5$ and $w = 5$ ft, then $l=5 + 5=10$ ft.

Step4: Calculate the area

The area formula of a rectangle is $A=l\times w$. Substitute $l = 10$ ft and $w = 5$ ft into the formula: $A=10\times5 = 50$ $ft^{2}$.

Answer:

50