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. Old garden area = New garden area x2 = (2x)(x – 16) x2 = 2x2 – 32x 0 = x2 – 32x What is the value of x that makes sense in this context? What are the dimensions of the new garden?

The quadratic equation that would model this scenario is[tex]x^{2} = 2x(x-16)[/tex]Let us take the side of the square = xArea of the square = x²Length of the rectangular garden = 2xWidth of the rectangular garden = x-16So, the area of the new vegetable garden = length*widthArea of the new or rectangular vegetable garden = 2x(x-16)What is a quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by [tex]ax^2+bx+c[/tex]coefficient [tex]x^{2}[/tex]non-zero.Since it is given thatArea of square garden = area of the rectangular garden[tex]x^{2} = 2x(x-16)[/tex]Thus, the quadratic equation that would model this scenario is[tex]x^{2} = 2x(x-16)[/tex]To get more about quadratic equations refer to: