Solve the problem.
-A right triangle has an area of 12 square inches. The square of the hypotenuse is 52. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.
A) 4 in. and 6 in.
B) 8 in. and 3 in.
C) 2 in. and 12 in.
D) 16 in. and 36 in.

Question

Quizplus · Accepted Answer

The area of a right triangle is given by (1/2) * base * height = 12 square inches. The square of the hypotenuse is 52, which means the hypotenuse is √52. Using the Pythagorean theorem, a^2 + b^2 = c^2, where c is the hypotenuse. Since the hypotenuse is √52, we know that a^2 + b^2 = 52. To find the legs that fit this description and also give an area of 12 square inches, we can test the options. Option A, 4 in. and 6 in., satisfies both conditions: (1/2) * 4 * 6 = 12 and 4^2 + 6^2 = 16 + 36 = 52.

Solve the Problem. -A Right Triangle Has an Area of 12 Square Inches