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 s
ame 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?
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.
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
