Question

The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation could be used to find the base (b) of the sign?

Answer 1

Comment
We should try the very simplest way of finding triangular areas first.

Formula
A = 1/2 b * h

Substitute
Area = 60 in^2
b = x
h = 2x - 1 
60= 1/2 * x * (2x - 1)

Solve
60 = 1/2 * x (2x - 1) Multiply by 2
60 * 2 = x(2x - 1)
120 = x (2x - 1) Remove the brackets.
120 = 2x^2 - x  Subtract 120 from both sides.
2x^2 -  x - 120 = 0 This factors.
(2x + 15)(x - 8) = 0

Solve for x
2x + 15 = 0
2x = - 15
x = -15/2
x = - 7.5 a negative measurement is useless. Discard this answer.

x - 8 = 0
x = 8 

Area (Check)
base = 8
height = 16 - 1 = 15

Area = 1/2 * 8 * 15 = 60 as it should

Answer
Use Area = 1/2 * b * h to find the base and the height.