One leg of a right-angled triangle is 5 m, the sum of the hypotenuse and the second leg is 25 m. Find the hypotenuse.

1. A, B, C – the vertices of the triangle. Angle A = 90 degrees. AC = 5 meters.
2. According to the condition of the problem AB + BC = 25 meters. Therefore, BC = 25 – AB.
3. AC² + AB² = BC² (by the Pythagorean theorem).
4. Substitute in this expression (25 – AB) instead of BC:
AC² + AB² = (25 – AB) ².
25 + AB² = 625 – 50 AB + AB².
50AB = 600.
AB = 12 meters.
BC = 25 – 12 = 13 meters.
Answer: The length of the BC hypotenuse is 13 meters.