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 does the value of x in her solutions represent?

one possible length and one possible width

two possible amounts for the widths

two possible amounts for the lengths

two possible amounts by which the dimensions were changed

Explanation:

The equation \((6 + x)(9 + x)=88\) models the situation where the original width is 6 ft and length is 9 ft, and \(x\) is the amount by which both length and width are increased. When solving this quadratic equation, the solutions for \(x\) represent the possible amounts (could be positive or negative, but in context, positive) by which the dimensions (length and width) were changed. The first option is wrong as \(x\) is not a length or width but the change. The second and third are wrong as \(x\) is the change for both, not separate amounts for width or length alone.

Answer:

two possible amounts by which the dimensions were changed