Question

Benjamin is doing some remodeling at his home. He currently has a triangular patio that has a base that is two times as long as its height. He wants to increase the length of the base of the patio by 4 feet and the length of the height of the patio by 9 feet. If x represents the height of the patio, which of the following functions will give the area of the new patio?

A.
f(x) = x2 + 11x + 18

B.
f(x) = x2 + 8.5x + 18

C.
f(x) = 2x2 + 36

D.
f(x) = 2x2 + 22x + 36

Answer 1

The new height is (x+9).
The new base is (2x+4).
The new area of the triangular patio is
f(x) = (1/2)*base*height
f(x) = (1/2)*(2x+4)(x+9) = (x+2)(x+9)

The appropriate choice is
A. f(x) = x² + 11x + 18