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

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

How to find the real dimensions of the rectangle?

The expression that represents the problem statement is;

x² = (2x)(x – 16)

Expanding the bracket gives us;

x² = 2x² – 32x

x² - 32x = 0

x(x - 32) = 0

Thus; x = 0 or x = 32

x can't be 0 and as such the value of x is 32.

Thus;

The length of the new garden is; l = 2x = 64.

The width of the new garden is; w = x - 16 = 32 - 16 = 16

The dimensions of the new garden are therefore; 64 by 16

Read more about Rectangle Dimensions at; brainly.com/question/17297081

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