Question

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. Old garden area = New garden area x2 = (2x)(x – 16) x2 = 2x2 – 32x 0 = x2 – 32x What is the value of x that makes sense in this context? What are the dimensions of the new garden?

Answer 1

The correct answer for Egdenuity students: 

x^2 = (2x)(x - 16) 

Answer 2

The value of x that makes sense in this context is; 32.

The dimensions of the new garden is; 64 by 16.

The expression which represents the problem statement is;

• x² = (2x)(x – 16)

• x² = 2x² – 32x

• x² - 32x = 0

• x (x - 32) = 0

x = 0 or x = 32

Logically, the value of x is therefore 32.

Therefore;

• The length of the new garden, l = 2x = 64.

• The width of the new garden, w = x -16 = 16

The dimensions of the new garden are; 64 by 16

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