Question

Assertion (A)
∆ABC ∼ ∆DEF, such that ar(∆ABC) = 100 cm² and ar(∆DEF) = 144 cm². If AB = 24 cm, then DE = 36 cm.
Reason (R)
If ∆ABC ∼ ∆DEF, then $\frac{\mathrm{ar}(∆ABC)}{\mathrm{ar}(∆DEF)}=\frac{A{B}^2}{D{E}^2}=\frac{B{C}^2}{E{F}^2}=\frac{A{C}^2}{D{F}^2}.$
(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

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

Reason (R) is clearly true.
$\because △ABC~∆DEF$

$\therefore \frac{ar(△ABC)}{ar(△DEF)}=\frac{A{B}^2}{D{E}^2}$
^{$$\begin{gathered} \Rightarrow \frac{100}{144}=\frac{A{B}^2}{D{E}^2} \\ \Rightarrow \frac{100}{144}=\frac{{24}^2}{D{E}^2} \\ \Rightarrow D{E}^2=\frac{144\times 576}{100} \\ \Rightarrow D{E}^{}=\frac{12\times 24}{10} \\ \Rightarrow D{E}^{}=28.8\ne 36 \end{gathered}$$}

Hence, Assertion (A) is false.