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The length of a rectangle is 1 foot more than twice the width. The area is 55 square feet. Find the length of the dimension of the rectangle.

User Krzakov
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1 Answer

17 votes
17 votes

Answer:

11 ft

Explanation:

The formula for the area of a rectangle of length L and width W is

A = L * W.

Represent the length, L, by 2W + 1 ("1 more than twice the width"). Then the area formula (above) becomes:

A = 55 ft^2 = (2W + 1)(W), which, when simplified, results in:

2W^2 + W - 55 = 0, whose coefficients are {2, 1, -55}. Let's use the quadratic formula to solve this for W:

The discriminant, b^2 - 4ac, is 1^2 - 4(2)(-55), or 441. The square root of 441 is 21. Thus, the quadratic formula gives us:

-1 ± 21

W = ------------- = (1/4)(-1 + 21), or W = 5 and W = -22/4 = -11/2

2(2)

A measure of length can't be negative, so we reject W = -11/2 in favor of W = 5.

Then, according to the formula for L that we found earlier, L = 2W + 1, or

L = 2(5) + 1, or L = 11.

Check: Does L * W result in an area of 55 ft²? Yes

The length dimension of the rectangle is 11 ft

User Bloodyaugust
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