1. **Problem statement:** We have a right triangle with one leg measuring 7 cm and the hypotenuse measuring 25 cm. We need to find: a) The length of the other leg. b) The area of the triangle. c) The perimeter of the triangle. 2. **Formula used:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the Pythagorean theorem states: $$a^2 + b^2 = c^2$$ The area $A$ of a right triangle is: $$A = \frac{1}{2} \times a \times b$$ The perimeter $P$ is: $$P = a + b + c$$ 3. **Find the other leg (b):** Given $a = 7$ cm and $c = 25$ cm, substitute into the Pythagorean theorem: $$7^2 + b^2 = 25^2$$ $$49 + b^2 = 625$$ $$b^2 = 625 - 49 = 576$$ $$b = \sqrt{576} = 24 \text{ cm}$$ 4. **Find the area:** $$A = \frac{1}{2} \times 7 \times 24 = \frac{1}{2} \times 168 = 84 \text{ cm}^2$$ 5. **Find the perimeter:** $$P = 7 + 24 + 25 = 56 \text{ cm}$$ **Final answers:** - Other leg length: $24$ cm - Area: $84$ cm$^2$ - Perimeter: $56$ cm