2012-02-10 09:00:31

What is the area of a right triangle whose hypotenuse is 20 and one of whose legs is 12?



The correct answer is 96

Explanation: First off, note that this question does not have answer choices, meaning it is a grid-in question, in which you’ll have to supply your own answer. To solve it, figure out what you have and what you need. We have the hypotenuse and one leg, and we need the area. The area of a triangle is ½ (base x height), meaning we need the other leg’s length to find the area. We can find this length by using the Pythagorean theorem: a² + b² = c². Here, let a = 12 and c = 20:

12² + b² = 20²                              This simplifies to            144 + b² = 400.

Subtract 144 from both sides to get b² = 256. Isolate b by square rooting both sides to get √b² = √256. Thus, b = 16. (Side note: expert test-takers might note that this creates a 3:4:5 right triangle, as 12:16:20 has the same ratio)

Now, use that number for the height to get the area of the triangle:

½ (12 x 16) = 96.                         Thus, the area of the triangle is 96.