Question

A rectangle's length and width are in a ratio of 5:1. The perimeter is 72 inches. What are the length and width?

length = inches

width = inches

Answer 1

Let the width be \( w \). According to the given ratio of length to width, the length \( l \) can be expressed as:

\[
l = 5w
\]

The formula for the perimeter \( P \) of a rectangle is:

\[
P = 2l + 2w
\]

Substituting the known perimeter (72 inches) into the equation, we have:

\[
72 = 2(5w) + 2w
\]

Simplifying this equation:

\[
72 = 10w + 2w
\]
\[
72 = 12w
\]

Now, solving for \( w \):

\[
w = \frac{72}{12} = 6 \text{ inches}
\]

Now, substituting \( w \) back into the equation for length:

\[
l = 5w = 5(6) = 30 \text{ inches}
\]

Thus, the dimensions of the rectangle are:

- Length = 30 inches
- Width = 6 inches

To summarize:

\[
\text{length} = 30 \text{ inches}
\]
\[
\text{width} = 6 \text{ inches}
\]