Problema Solution
The height of a triangle is 4 inches greater than twice its base. The area of the triangle is 168 square inches. What is the base of the triangle?
Answer provided by our tutors
Area of a triangle is 1/2 * base * height. In this case, you know area = 168 and height = 2*base + 4,so you write two equations using variables as follows:
A = area, b = base, h = height
A = 168 = 1/2 * b * h
h = 2b + 4
substitute the second equation into the first
168 = 1/2 * b * (2b + 4)
168 = b^2 + 2b
b^2 + 2b -168 = 0
(b-12)(b+14) = 0
b = 12 (or -14, but -14 not allowed)
Answer is c, b= 12in.