The legs of a right triangle are 7 and 24. Find the hypotenuse of this triangle.

Let $$a$$ and $$b$$ be the lengths of the legs of the right triangle, and let $$c$$ be the length of the hypotenuse. According to the Pythagorean theorem, we have:

$$a^2 + b^2 = c^2$$

Given that $$a = 7$$ and $$b = 24$$, we can find $$c$$:

$$7^2 + 24^2 = c^2$$

$$49 + 576 = c^2$$

$$625 = c^2$$

$$c = \sqrt{625}$$

$$c = 25$$

Answer: 25