The area of a right triangle is 270 square meters. The height of the right triangle is 15 meters.

What is the length of the hypotenuse of the right triangle?

Enter your answer in the box.

m

To solve this, we find the measure of the base using the the formula for the area of a triangle. Then plug both of these into the Pythagorean theorem to solve for the hypotenuse.

Area of a triangle = 1/2 * base * height

270 = 1/2 * 15 * base

270 = (15 / 2) (base)

270 (2 / 15) = base

540 / 15 = base

36 = base

Now, we plug into the Pythagorean Theorem of a² + b² = c² where a and b are the legs of the triangle (AKA the base and height) and c is the hypotenuse.

15² + 36² = c²

225 + 1296 = c²

1521 = c²

√c² = √1521

c = √1521

c = 39

The length of your hypotenuse is 39 meters.