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.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) inches. Then the length \( l \) is \( 3w \) inches (since length is three times the width).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 40 \) inches. Substitute \( l = 3w \) into the formula:
\[
40 = 2(3w + w)
\]

Step3: Simplify and solve for \( w \)

First, simplify the expression inside the parentheses: \( 3w + w = 4w \). So the equation becomes:
\[
40 = 2(4w)
\]
\[
40 = 8w
\]
Divide both sides by 8:
\[
w = \frac{40}{8} = 5
\]

Step4: Find the length

Since \( l = 3w \), substitute \( w = 5 \):
\[
l = 3 \times 5 = 15
\]

Answer:

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