Question

A rectangular patio is 9 ft by 6 ft. When the length amd width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6+x)(9+x)= 88. What do her solutions represent?

Answer 1

( 6 + x)(9 + x) =88

54 + 15x + x^2 = 88

x^2 + 15x - 34 = 0

(x + 17)(x - 2) = 0
using zero product property:-
x + 17 =  0  or x - 2 = 0    giving:-

x = -17 , x = 2

x is the amount that the length and width are increased by.

x = -17 is negative and doesn't make sense in this context  and can be ignored; so the amount of increase is  2 feet.