Answer:
The width of the rectangle is approximately 8.904 yards, and the length of the rectangle is 24.71 yards.
Explanation:
Let x be the width of the rectangle, then the length of the rectangle is 4x - 18.
The area of the rectangle is x * (4x - 18) = 630, so we can solve for x:
x * (4x - 18) = 630
Expanding and rearranging the equation:
4x^2 - 18x - 630 = 0
Using the quadratic formula, we can find the solutions for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a = 4, b = -18, and c = -630.
x = (18 ± √(18^2 - 4 * 4 * -630)) / (2 * 4)
x = (18 ± √(18^2 + 2520)) / 8
x = (18 ± √(324 + 2520)) / 8
x = (18 ± √2844) / 8
x = (18 ± 53.23) / 8
Since width can't be negative, x must be positive, so:
x = (18 + 53.23) / 8
x = 71.23 / 8
x = 8.904
The length of the rectangle is 4 * 8.904 - 18 = 24.71 yards.