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

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.

Answer 2

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