Question

A rectangle with an area of 40 square yards has a length and width in a ratio of 10:1. What are the length and width?

length =
yards

width =
yards

Answer 1

Let the width be \( w \) yards. Since the ratio of the length to the width is 10:1, we can express the length as \( 10w \).

The area of the rectangle is given by the formula:

\[
\text{Area} = \text{length} \times \text{width}
\]

We know the area is 40 square yards, so we can set up the equation:

\[
10w \times w = 40
\]

This simplifies to:

\[
10w^2 = 40
\]

Now, divide both sides by 10:

\[
w^2 = 4
\]

Taking the square root of both sides, we find:

\[
w = 2 \quad (\text{since width must be positive})
\]

Now, we can find the length:

\[
\text{length} = 10w = 10 \times 2 = 20
\]

Thus, the dimensions of the rectangle are:

\[
\text{length} = 20 \text{ yards}
\]

\[
\text{width} = 2 \text{ yards}
\]