Question

Assertion (A): x = `5sqrt2`.

Reason (R): AC² = 8² + 6² = x² + x²

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, and R is the incorrect reason for A.

Answer 1

Both A and R are true, and R is the correct reason for A.

Explanation:

• Assertion (A): In right-angled ΔABC, AC² = 8² + 6² = 64 + 36 = 100, meaning AC = 10. In right-angled ΔADC, AC² = x² + x² = 2x². Equating the two gives 2x² = 100, which simplifies to x² = 50 or x = `sqrt50 = 5sqrt2`, confirming that Assertion (A) is true.
• Reason (R): The statement correctly equates the square of the shared diagonal $AC$ obtained from both right-angled triangles (ΔABC and ΔADC), establishing the valid mathematical relationship 8² + 6² = x² + x² that directly solves for Assertion (A).