Question

the length of a rectangle is 3 in longer than its width.
if the perimeter of the rectangle is 30 in, find its area.
$square in^{2}$

Explanation:

Step1: Let the width be \(x\)

Let the width of the rectangle be \(x\) inches. Then the length is \((x + 3)\) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \(P=2(l + w)\). Given \(P = 30\) in. So, \(2(x+(x + 3))=30\).
Simplify the equation:

$$
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$$

Step3: Find the length

Since \(x = 6\), the length \(l=x + 3=6+3 = 9\) inches.

Step4: Calculate the area

The area formula for a rectangle is \(A=l\times w\). Substitute \(l = 9\) and \(w = 6\)
\(A=9\times6=54\)

Answer:

\(54\)