The height of a triangle is 8 centimeters greater than three times its base.

Question

The height of a triangle is 8 centimeters greater than three times its base. The area of the triangle is 128 square centimeters. What is the base of the triangle?

The answer I got was 8 cm.

Answer 1

Hi Jean,

Looks right to me. Let x = length of base. Therefore altitude = 3x+8.

Using A = 1/2 bh gives 128 = 1/2 (x)(3x+8).

This results in 3x²+8x-256 = 0.

Solving for x (factoring, completing the square, or quadratic formula) results in x=8 or x=-32/3. Latter can be rejected based on the problem being solved (length of segment cannot be negative).