Question

Assertion: In a quadrilateral ABCD, we have (AB + BC + CD + DA) > 2AC.

Reason: The sum of any two sides of a triangle is greater than the third side.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
We know that sum of any two sides of a triangle is greater than the third side.
Therefore, $\left(AB+BC\right)>AC$ and $\left(CD+DA\right)>AC$.
Adding them, we get:
$(AB+BC+CD+DA)>2AC$
Thus, the assertion is true, and the reason gives the assertion.