1. **State the problem:** We have a right triangle with one side length of 24 cm. We need to determine which pair of lengths from the options can be the other two sides of the triangle. 2. **Recall the Pythagorean theorem:** For a right triangle with sides $a$, $b$, and hypotenuse $c$, the relationship is: $$a^2 + b^2 = c^2$$ where $c$ is the longest side. 3. **Check each option:** We must identify if 24 is the hypotenuse or one of the legs and verify if the Pythagorean theorem holds. - Option A: 7 cm and 25 cm - If 25 is hypotenuse: Check $7^2 + 24^2 = 25^2$ - Calculate: $49 + 576 = 625$ - $625 = 625$ ✓ Valid - Option B: 8 cm and 23 cm - Hypotenuse candidate is 24 or 23? 24 is longer, so 24 could be hypotenuse. - Check $8^2 + 23^2 = 24^2$ - Calculate: $64 + 529 = 576$ - $593 \neq 576$ ✗ Not valid - Option C: 9 cm and 22 cm - Check $9^2 + 22^2 = 24^2$ - Calculate: $81 + 484 = 576$ - $565 \neq 576$ ✗ Not valid - Option D: 10 cm and 27 cm - 27 is longer than 24, so 27 could be hypotenuse. - Check $10^2 + 24^2 = 27^2$ - Calculate: $100 + 576 = 729$ - $676 \neq 729$ ✗ Not valid 4. **Conclusion:** Only option A satisfies the Pythagorean theorem with 24 as one leg and 25 as the hypotenuse. **Final answer:** The other two sides could be 7 cm and 25 cm.