A right triangle has an area of 120 square units, and a leg length of 24 units. What is the perimeter of the triangle, in units?
I already know one leg is 24 units, so I need to find the other leg and the hypotenuse. The area of a right triangle is half the product of the lengths of the legs, so I can use that formula to find the other leg. The area is 120 square units, so I can write the equation 120 = (1/2)(24)(x), where x is the other leg. Solving for x, I get x = (120 * 2) / 24 = 10 units. So the other leg is 10 units long. To find the hypotenuse, I can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the legs. Letting h be the hypotenuse, I get h^2 = 24^2 + 10^2. Simplifying, I get h^2 = 676. Taking the square root of both sides, I get h = 26 units. So the hypotenuse is 26 units long. Now I have all the side lengths, so I can find the perimeter by adding them up. The perimeter is 24 + 10 + 26 = 60 units. 