The length of a rectangle is 8 in. more than twice its width. Its area is 154 in². Find the length of the rectangle. A) 7 in. B) 22 in. C) 30 in. D) 484 in. E) 44 in.

Question

Quizplus · Accepted Answer

Let's say the width of the rectangle is "x". According to the problem, the length is "8 in. more than twice its width", which can be expressed as "2x + 8". We also know that the area of the rectangle is 154 in². The formula for the area of a rectangle is length times width, so we can write an equation:
A = lw
154 = x(2x + 8)
Expanding the brackets and rearranging the terms, we get:
2x² + 8x - 154 = 0
Dividing both sides by 2, we get:
x² + 4x - 77 = 0
This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula. One possible factorization is:
(x - 7)(x + 11) = 0
This gives us two solutions: x = 7 or x = -11. Since the width of the rectangle can't be negative, we reject the negative solution and conclude that the width is 7 in. To find the length, we use the expression we derived earlier:
length = 2x + 8
length = 2(7) + 8
length = 22
Therefore, the length of the rectangle is 22 in.

The Length of a Rectangle Is 8 In