Question

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

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) inches. Then the length \( l = 3w \) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Given \( P = 40 \) inches. Substitute \( l = 3w \) into the formula: \( 40=2(3w+w) \).
Simplify the right - hand side: \( 40 = 2\times4w\), so \( 40=8w \).

Step3: Solve for \( w \)

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

Step4: Solve for \( l \)

Since \( l = 3w \), substitute \( w = 5 \) into the equation: \( l=3\times5 = 15 \) inches.

Answer:

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