Assertion (A): The perimeter of $\triangle ABC$ is a rational number. Reason (R): The sum of the squares of two rational numbers is always rational.
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Option (D): Assertion (A) is false but Reason (R) is true.
AC = $\sqrt{AB^2 + BC^2} = \sqrt{4+9} = \sqrt{13}$ (irrational). So perimeter = $2 + 3 + \sqrt{13}$ is irrational, making A false. R is true since sum of squares of two rationals is always rational.
Explanation
- Check AC using Pythagoras: $\sqrt{2^2+3^2}=\sqrt{13}$, which is irrational (13 is not a perfect square).
- Perimeter = rational + irrational = irrational → Assertion is false.
- Reason: $\left(\frac{p}{q}\right)^2 + \left(\frac{a}{b}\right)^2$ is always rational → Reason is true.
- R does not explain A (since A itself is false), so answer is (D).