In a right-angled triangle, the hypotenuse is 10 inches and one of the other sides is 6 inches. What is the area of the triangle?
Correct: C
Using the Pythagorean Theorem to find the other leg: a^2 + b^2 = c^2, where c = 10 (hypotenuse) and one leg (let's say a) = 6. Thus, 6^2 + b^2 = 10^2. This gives 36 + b^2 = 100. Solving for b^2 gives b^2 = 64, and hence b = 8. The area of a triangle is given by 1/2 * base * height. In a right triangle, the two legs can serve as the base and height. Therefore, the area = 1/2 * 6 * 8 = 24 square inches.