Question

A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation:

Answer 1

Length = x
width = x-2

area of a rectangle = L x W

area = 48

so you have x * (x-2) = 48

simplify the left side :
x^2 -2x = 48

subtract 48 from both sides:

x^2 - 2x -48 = 0

now factor the polynomial:

(x-8) (x+6)
solve for x:
x-8 = 0. x = 8
x+6 = 0, x=-6

you can't have a length which is a negative number so x ( the length) = 8 feet

the width = 8-2 = 6 feet

8 * 6 = 48 so this is true.

Length = 8 feet, width = 6 feet