Question

the length of a rectangle is three times its width. if the area of the rectangle is 147 in², find its perimeter. in

Explanation:

Step1: Let the width of the rectangle be \( w \)

Let the width of the rectangle be \( w \) inches. Since the length \( l \) is three times its width, \( l = 3w \).
The area formula of a rectangle is \( A=l\times w \). Given \( A = 147\space in^{2} \), substitute \( l = 3w \) into the area formula: \( 147=(3w)\times w\).

Step2: Solve for \( w \)

Simplify the equation \( 147 = 3w^{2}\). Divide both sides by 3: \( w^{2}=\frac{147}{3}=49 \). Take the square - root of both sides. Since \( w>0 \) (width cannot be negative), \( w = 7\space in \).

Step3: Find the length

Since \( l = 3w \), substitute \( w = 7 \) into the equation. Then \( l=3\times7 = 21\space in \).

Step4: Calculate the perimeter

The perimeter formula of a rectangle is \( P=2(l + w) \). Substitute \( l = 21 \) and \( w = 7 \) into the formula: \( P=2(21 + 7)=2\times28\).

Answer:

\( 56 \)