Question

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 ft2. Which quadratic equation best models the situation?

A = lw
(15)(12) + (x)(x) = (15)(12) + 160
(15x)(12x) = (15)(12) + 160
2(15 + x) + 2(12 + x) = (15)(12) + 160
(15 + x)(12 + x) = (15)(12) + 160

Answer 1

Use A = lw. New area = (15 + x)(12 + x) and it equals original area 180 plus 160 = 340. So
(15 + x)(12 + x) = 340,
which expands to
x^2 + 27x - 160 = 0.

Thus the correct choice is (15 + x)(12 + x) = (15)(12) + 160.