To find the dimensions of the rectangle, we can start by setting up the relationship based on the ratio and the area.
Let the length be \( 15x \) and the width be \( 8x \), where \( x \) is a common factor. The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
Substituting the expressions for length and width into the area formula gives us:
\[ 480 = (15x)(8x) \]
This simplifies to:
\[ 480 = 120x^2 \]
Next, we can solve for \( x^2 \) by dividing both sides of the equation by 120:
\[ x^2 = \frac{480}{120} \]
Calculating the right side:
\[ x^2 = 4 \]
Taking the square root of both sides gives us:
\[ x = 2 \]
Now, we can find the length and width using the value of \( x \):
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Length: \[ \text{Length} = 15x = 15 \times 2 = 30 \text{ yards} \]
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Width: \[ \text{Width} = 8x = 8 \times 2 = 16 \text{ yards} \]
Thus, the dimensions of the rectangle are:
Length = 30 yards
Width = 16 yards