Question

the length of a rectangle is three times its width. if the area of the rectangle is 147 m², find its perimeter.

Explanation:

Step1: Set up variables

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

Step2: Use the area formula

The area formula for a rectangle is \(A = length\times width\). So \(147=3x\times x\), which simplifies to \(3x^{2}=147\). Divide both sides by 3: \(x^{2}=\frac{147}{3}=49\). Take the square root of both sides: \(x = 7\) (we take the positive value since length cannot be negative).

Step3: Find length and width

Width \(x = 7\) m, length \(3x=3\times7 = 21\) m.

Step4: Use the perimeter formula

The perimeter formula for a rectangle is \(P=2\times(length + width)\). So \(P = 2\times(21 + 7)=2\times28 = 56\) m.

Answer:

\(56\) m