Answer:
11 ft
Step-by-step 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
