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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?

User Kyanny
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the answer is a. x^2+(2x)(x-16)

User Arrehman
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Short Answer: x^2 - 32x = 0
Square garden has a side of x
Area of the square garden is x^2

The length of the rectangle = 2x
The width is x - 16
Area of the rectangular garden is 2x(x - 16)
Area of the rectangular garden is 2x^2 - 32x

The area of the square and the rectangle must remain the same.
2x^2 - 32x = x^2 Subtract x^2 from both sides.
2x^2 - x^2 - 32x = 0

x^2 - 32x = 0 Technically this is the answer to your question.


User Ratha
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