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Question

Assertion (A)
In an isosceles ∆ABC, if ∠C = 90°, then AB2 = 3AC2.
Reason (R)
In an isosceles ∆ABC, if AC = BC and AB2 = 2AC2, then ∠C = 90°.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A)
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

(d) Assertion (A) is false and Reason (R) is true.

In triangle ABC, let BC be equal to AC.
We have:
C = 90°
Thus,
AB2 = AC2 + BC2 = AC2 + AC2 ( AC = BC) AB2 = 2AC2

Assertion (A) is false.
This proves that Reason (R) is true.

Hence, Assertion (A) is false and Reason (R) is true.

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