Question

the length of a rectangle is three times its width. if the perimeter of the rectangle is 40 m, find its length and width. length: m width: m

Explanation:

Step1: Set up variables

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

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \(P = 2(l + w)\). Given \(P=40\) m, substitute \(l = 3x\) and \(w=x\) into the formula:
\(40=2(3x + x)\)
Simplify the right - hand side: \(40 = 2\times4x\), so \(40=8x\)

Step3: Solve for \(x\)

Divide both sides of the equation \(40 = 8x\) by 8: \(x=\frac{40}{8}=5\)

Step4: Find the length

Since the length \(l = 3x\), substitute \(x = 5\) into it. Then \(l=3\times5 = 15\)

Answer:

length: \(15\) m, width: \(5\) m