06/19/2020 (2011: Countdown Round, Problem 12)

Q: The sides of a triangle are in the ratio of 5:12:13. What is the area of the triangle, in square units, if its perimeter is 80 units? Express your answer as a common fraction.

A: 640/3

The side lengths are 5x, 12x, and 13x. That means that the perimeter is 30x = 80. That means x = 8/3, so the legs' lengths are 40/3 and 32 units. The area is 40/3 * 32 ÷ 2 = 640/3.