The davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. they want to extend the length and width the same amount to increase the total area of the patio by 160 ft^2.
which quadratic equation best models the situation?

a. (15)(12)+(x)(x) = (15)(12) + 160
b. (15x)(12x)=(15)(12) + 160
c. 2(15+x) + 2(12+x) = (15)(12) + 160
d. (15 + x)(12 + x) = (15)(12) + 160

d.

Step-by-step explanation:

We originally have a patio that measures 15 ft by 12ft.

The area of this patio is given by the multiplication of the measurements, so the original area of the patio is:

We want to increase the same amount of each of the sides, if we call this amount :

multiplying these two quantities should result in the final area of the patio which we know should be the original area plus the increase in area because the sides were lengthened. This increase in area according to the problem is , so the final area, and the quadratic equation that best models the situation is:

the sides extended by an amount when multiplied result in the original area added to an increase in the area due to the extension of the sides that according to the problem is 160.

The answer is d.