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:
\[ \text{length} = 20 \text{ yards} \]
\[ \text{width} = 2 \text{ yards} \]