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?
Accepted Solution
A:
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.