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?

Answer 1

you did not provide answer choices but I think it would be D. two possible amounts by which the dimensions were increased.

Answer 2

Answer:

Step-by-step explanation:

Multiply out  (6 + x)(9 + x) and set the result (product) = to 88 ft²:

54 + 9x + 6x + x² = 88 ft².

Then 54 + 15x + x² - 88 ft² = 0

Combining the constants, we get x² + 15x - 34 = 0

This factors easily to (x + 17)(x - 2) = 0, with the result that x = 2.

We conclude that if we increase both the 9 ft length and the 6 ft width by 2 ft, the new area will be 88 ft².  Note that (9+2)(6+2) = 88.

We discard the x-value -17, as we are ADDING the quantity x to the original measurements (9 by 6 ft) to obtain new measurements (11 by 8 ft).