Question

The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?

Answer 1

Area = (1/2)(base)(height) ≤ 168. With height = 2x + 4:
(1/2)x(2x + 4) ≤ 168

Simplify: x^2 + 2x ≤ 168 → x^2 + 2x − 168 ≤ 0 → (x + 14)(x − 12) ≤ 0

So −14 ≤ x ≤ 12. Since a base length must be positive, 0 < x ≤ 12 inches.