Paper 1 · Mathematical Reasoning and Aptitude
UGC NET December 2021 June 2022 (11.10.2022) Shift-I
Given below are two statements. Statement I: If you know the length of any one side of a right-angled triangle, the area of the triangle can be found. Statement II: If you know the lengths of two sides of a right-angled triangle, the length of the third side can be found. In the light of the above statements, choose the most appropriate answer from the options given below.
- Statement I: Knowing one side of a right-angled triangle lets you find its area.
- Statement II: Knowing two sides of a right-angled triangle lets you find the third side.
ABoth Statement I and Statement II are correct
BBoth Statement I and Statement II are incorrect
CStatement I is correct but Statement II is incorrect
DStatement I is incorrect but Statement II is correct ✓ Correct
Correct answer: (D) Statement I is incorrect but Statement II is correct — The answer is that Statement I is incorrect but Statement II is correct.
Explanation
★The answer is that Statement I is incorrect but Statement II is correct.
★Knowing just one side of a right-angled triangle does not fix its area.
★So Statement I is incorrect.
★By the Pythagoras theorem, knowing two sides lets you compute the third side.
★So Statement II is correct.
★Thus only the second statement holds.
★So the answer is that Statement I is incorrect but Statement II is correct.
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