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Question

Assertion (A)
∆ABC ∼ ∆DEF such that BC = 4.5 cm and EF = 3.5 cm and ar(∆ABC) = 81 cm2, then ar(∆DEF) = 49 cm2.
Reason (R)
The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians.

(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

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

The Reason(R) is clearly true.
∆ABC ∼ ∆DEF

ar(ABC)ar(DEF) = BC2EF2 81ar(DEF) = 4.523.52 ar(DEF) = 81 × 3.5 × 3.54.5 × 4.5 = 49 cm2

Hence, Assertion (A) is true but Reason (R) is not the correct explanation of (A).

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