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.

Answer 1

(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.
$\because$ ∆ABC ∼ ∆DEF

$$\begin{gathered} \therefore \frac{ar(△ABC)}{ar(△DEF)}=\frac{B{C}^2}{E{F}^2} \\ \Rightarrow \frac{81}{ar(△DEF)}=\frac{4.5^2}{3.5^2} \\ \Rightarrow ar(△DEF)=\frac{81\times 3.5\times 3.5}{4.5\times 4.5}=49{\mathrm{cm}}^2 \end{gathered}$$

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