AnswersCommon Core Algebra I 2014 - MA3109 B-CRSolving Quadratic Equations: Completing the SquareQuestion 5
5
AssignmentMultiple Choice

Solving Quadratic Equations: Completing the Square

Question 5 • Common Core Algebra I 2014 - MA3109 B-CR

Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario?

Answer
A
x2 = (2x)(x – 16)
B
x2 = (x)(x – 16)
C
x2 = (x)(x + 16)
D
x2 = (2x)(x + 16)

Explanation

The square garden has area x × x = x². The new rectangle’s length is 2x, and its width is 16 feet less than the square’s side length, or x − 16. Since the gardens must have the same area, set x² equal to the rectangle’s area: x² = (2x)(x − 16). This is the equation in choice A.

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