Real numbers
Grade Class 10
Question:
<p><strong>Assertion (A):</strong> The perimeter of <span class="math-tex">\(\triangle\)</span>ABC is a rational number.<br />
<strong>Reason (R):</strong> The sum of the squares of two rational numbers is always rational.<br />
<img src="https://media-mycbseguide.s3.amazonaws.com/images/question_images/1688640626-r6xy3a.jpg" style="height:113px; width:200px" /></p>
<p style="display:inline">Both A and R are true and R is the correct explanation of A.</p>
<p style="display:inline">Both A and R are true but R is not the correct explanation of A.</p>
<p style="display:inline">A is true but R is false.</p>
<p style="display:inline">A is false but R is true.</p>
Step-by-Step Solution
Key Concept: While the sum of squares of rational coordinate differences is always rational, the resulting side lengths involve square roots which are often irrational, making the perimeter irrational.
<p>A is false but R is true.</p>
Correct Answer: D