1. **Problem Statement:** Find the length of side AB in a right triangle $\triangle ABC$ where $\angle B = 90^\circ$, hypotenuse $AC = 25$ cm, and one leg $BC = 24$ cm. 2. **Formula Used:** In a right triangle, the Pythagorean theorem states: $$AB^2 + BC^2 = AC^2$$ where $AC$ is the hypotenuse. 3. **Step-by-step Solution:** - Given $AC = 25$ cm and $BC = 24$ cm. - Substitute into the Pythagorean theorem: $$AB^2 + 24^2 = 25^2$$ - Calculate squares: $$AB^2 + 576 = 625$$ - Isolate $AB^2$: $$AB^2 = 625 - 576 = 49$$ - Take the square root: $$AB = \sqrt{49} = 7$$ 4. **Answer:** The length of side $AB$ is $7$ cm. This means the triangle sides are 7 cm, 24 cm, and 25 cm, satisfying the Pythagorean theorem.