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?

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.