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: Let the width be \(x\)

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

Step2: Use the area formula

The area formula of a rectangle is \(A = length\times width\). Given \(A = 147\space m^{2}\), so \(3x\times x=147\), 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 width cannot be negative).

Step3: Find the length

Since length \(l = 3x\), substituting \(x = 7\), we get \(l=3\times7 = 21\space m\).

Step4: Use the perimeter formula

The perimeter formula of a rectangle is \(P=2(l + w)\). Substitute \(l = 21\) and \(w = 7\): \(P=2(21 + 7)=2\times28 = 56\space m\).

Answer:

\(56\space m\)