A rectangular patio is 9 ft by 6 ft. When the length and 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?
a.one possible length and one possible width
b.two possible amounts for the widths
c.two possible amounts for the lengths
d.two possible amounts by which the dimensions were increased

Question

A rectangular patio is 9 ft by 6 ft. When the length and 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?
a.one possible length and one possible width
b.two possible amounts for the widths
c.two possible amounts for the lengths
d.two possible amounts by which the dimensions were increased

boldjon · Answer

I THINK ItS D

phi · Answer

if we multiply out (x+6)(x+9) we will get a quadratic
$$ x^2 +15x + 54 $$
and an equation
$$ x^2 +15x + 54=88 \ x^2 +15x -34=0 $$
we will get two different numbers for x
so that means 2 different widths and two different lengths

yes, D

boldjon · Answer

k thanks

phi · Answer

although I just solved the quadratic, and got
x=-17 and x= 3

realistically, we don't add -17 to the length.
So this might be a trick question and the answer is A .

phi · Answer

*x= -17 and x=2  
only the x=2 solution makes sense.