1. The problem asks us to verify the Pythagorean Theorem for a right triangle with legs 6 cm and 8 cm. 2. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse ($c$) equals the sum of the squares of the legs ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. Here, the legs are $a=6$ cm and $b=8$ cm. We need to check if the sum of their squares equals the square of the hypotenuse. 4. Calculate the squares of the legs: $$6^2 = 36$$ $$8^2 = 64$$ 5. Sum these squares: $$36 + 64 = 100$$ 6. Now, find the square root of 100 to get the hypotenuse: $$c = \sqrt{100} = 10$$ 7. Check the options: - Option A: $6 + 8 = 14$ (This is just the sum of legs, not related to the theorem) - Option B: $62 + 82 = 142$ (Incorrect notation and incorrect sum) - Option C: $(6 + 8)^2 = 6^2 + 8^2$ (Incorrect, the square of the sum is not equal to the sum of squares) - Option D: $62 + 82 = 36 + 64 = 100 = 10^2$ (Correctly shows the sum of squares equals the square of the hypotenuse) 8. Therefore, option D correctly verifies the Pythagorean Theorem for this triangle.