What is the length of the base of the triangle?

Question

The length of the base of  triangle is 1 more than twice it's height. The area of the triangle is 18in^2. What is the length of the base of the triangle?

Answer 1

Let h = the height

Let 2h + 1 = the length of the base

A = 1/2 bh

18 = 1/2 h(2h+1)     Multiply both sides by 2.

36 = 2h² + h

2h² + h -36 = 0

(2h+9)(h-4) = 0

2h + 9 = 0     or    h - 4 = 0

       2h = -9               h = 4 inches

         h = -9/2 (illogical answer)

base = 2h + 1 = 2(4) + 1 = 8 + 1

base = 9 inches