the width of a rectangle is 7 feet less than it's length. if the area of the rectangle is 170 square feet, then find the length and width

let length = x

width is 7 feet less than length

width = x-7

area = length * width

area = x (x-7)

170=x²-7x

x²-7x-170=0

x²-17x+10x-170=0

x (x-17) + 10 (x-17) = 0

(x-17) (x+10) = 0

x=17 or x=-10

since length cannot be negative so x=17

and width = x-7 = 17-7=10

length = 17 feet and width = 10 feet