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Consider the following statements about a right-angled triangle: Statement-1: For any right-angled triangle, the value of (a²+b²+c²)/R² is always 8. Statement-2: a²=b²+c². Choose the correct option.

1. Statement-1 is true, Statement-2 is true; Statement-2 correctly explains Statement-1
2. Statement-1 is true, Statement-2 is true; Statement-2 does not correctly explain Statement-1
3. Statement-1 is false, Statement-2 is true
4. Statement-1 is true, Statement-2 is false

Correct answer: Statement-1 is true, Statement-2 is true; Statement-2 correctly explains Statement-1

Solution

For a right triangle the hypotenuse a=2R, so a^2=4R^2 and b^2+c^2=a^2=4R^2, giving (a^2+b^2+c^2)/R^2 = 8R^2/R^2 = 8. Statement-1 is true only because a^2=b^2+c^2 (Statement-2) holds, so both are true and S2 correctly explains S1.

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