The hypotenuse of a 45-45-90 triangle measures 24 inches. What is the length of one leg of the triangle?

To find the length of one leg of a 45-45-90 triangle when you know the length of the hypotenuse, you can use the properties of this special type of right triangle. In a 45-45-90 triangle, the legs are congruent (meaning they have the same length), and the lengths of the legs are each equal to the length of the hypotenuse divided by the square root of 2. This follows from the Pythagorean theorem, as each leg (let's call it "L") and the hypotenuse (let's call it "H") satisfy the equation L^2 + L^2 = H^2 for a right triangle.

Let's calculate the length of one leg, given that the hypotenuse (H) is 24 inches:

L = H / √2

Now plug in the length of the hypotenuse:

L = 24 inches / √2

To rationalize the denominator, you can multiply the numerator and the denominator by √2:

L = (24√2) / 2

Now, simplify:

L = (24/2) * (√2/√2)

L = 12√2

The length of one leg in the triangle is 12√2 inches.