Question

the length of a rectangle is five times its width. if the perimeter of the rectangle is 108 yd, find its length and width. length: yd width: yd

Explanation:

Step1: Let the width of the rectangle be \(x\) yd.

Since the length is five times the width, the length is \(5x\) yd.

Step2: Use the perimeter formula for a rectangle \(P = 2(l + w)\).

Given \(P=108\) yd, \(l = 5x\), and \(w=x\). Substitute into the formula: \(108=2(5x + x)\).
Simplify the right - hand side: \(108 = 2\times6x\), so \(108=12x\).

Step3: Solve for \(x\).

Divide both sides of the equation \(108 = 12x\) by 12: \(x=\frac{108}{12}=9\).

Step4: Find the length.

Since the length \(l = 5x\), substitute \(x = 9\) into \(l = 5x\). Then \(l=5\times9 = 45\).

Answer:

length: \(45\) yd
width: \(9\) yd