Triangle word problem

Question

The base of a triangle is 5 inches shorter than 2 times it's height. The area of the triangle is 114. I keep getting the height is a negative number.

Answer 1

Let h = height and b = base

b = 2h -5

Area = (1/2)bh = (1/2)h(2h - 5) = 114

$2h^2-5h-228=0$

The quadratic formula gives an extraneous root at h = 12

b = 19