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A rectangle has a length pf 18 yards less than 4 times its width. if the area of the rectangle is 630 yards, find the length of the rectangle

User Xlembouras
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1 Answer

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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.

User Dennis Calla
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