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?

Question

Mathematics

Tiara Russo

26 May, 21:35

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?

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Answers (2)

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Rosa King · Answer 1

Here is the model, but the Areas are not the same.

Old = X*X = X^2 Area

New = 2X * (X-16) = 2X^2-32X

If the Areas are the same,

2X^2 - 32X = X^2

X^2 - 32X = 0

X (X-32) = 0

X = 32

Old Area = 32x32 = 1024 ft^2

New Area = 2 (32x32) = 32x32 = 1024 ft^2

Athena Cruz · Answer 2

For the square, the area will be 4x4, which will equal 16 sq ft. Since Juan is wanting to turn it to a rectangle, he will have to use the equation 8x2.