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? x2 = (2x)(x – 16) x2 = (x)(x – 16) x2 = (x)(x 16) x2 = (2x)(x 16).

Answer 1

The quadratic equation that would model this scenario is

$x^{2} = 2x(x-16)$

Let us take the side of the square = x

Area of the square = x²

Length of the rectangular garden = 2x

Width of the rectangular garden = x-16

So, the area of the new vegetable garden = length*width

Area 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 $ax^2+bx+c$coefficient $x^{2}$non-zero.

Since it is given that

Area of square garden = area of the rectangular garden

$x^{2} = 2x(x-16)$

Thus, the quadratic equation that would model this scenario is

$x^{2} = 2x(x-16)$

To get more about quadratic equations refer to:

brainly.com/question/1214333