The height of a right-angled triangle, drawn from a right angle, is 5 cm, one of the legs is 13 cm. Find the hypotenuse.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. Height CE = 5 centimeters. BC = 8 centimeters.

2. We calculate the length of the segment BE:

BE = √BC² – CE² = √13² – 5² = √169 – 25 = √144 = 12 centimeters.

3. We calculate the length of the segment AE, applying the formula for calculating the length of the height CE, drawn from

vertices of an angle equal to 90 °:

CE = √AE x BE.

CE² = AE x BE.

AE = CE²: BE = 25: 12 = 2.5 centimeters.

4. AB = AE + BE = 2.5 + 12 = 14.5 centimeters.

Answer: The length of the hypotenuse is 14.5 centimeters.