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. What is the quadratic equation that would model this scenario?

Answer 1

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.

Answer 2

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