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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 $\frac{\mathrm{ar}\left(∆ABC\right)}{\mathrm{ar}\left(∆DEF\right)}=\frac{A{B}^{2}}{D{E}^{2}}=\frac{B{C}^{2}}{E{F}^{2}}=\frac{A{C}^{2}}{D{F}^{2}}.$ (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.

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Solution

## (d) Assertion (A) is false and Reason (R) is true. Reason (R) is clearly true. $\because △ABC~∆DEF$ $\therefore \frac{ar\left(△ABC\right)}{ar\left(△DEF\right)}=\frac{A{B}^{2}}{D{E}^{2}}$ $⇒\frac{100}{144}=\frac{A{B}^{2}}{D{E}^{2}}\phantom{\rule{0ex}{0ex}}⇒\frac{100}{144}=\frac{{24}^{2}}{D{E}^{2}}\phantom{\rule{0ex}{0ex}}⇒D{E}^{2}=\frac{144×576}{100}\phantom{\rule{0ex}{0ex}}⇒D{E}^{}=\frac{12×24}{10}\phantom{\rule{0ex}{0ex}}⇒D{E}^{}=28.8\ne 36$ Hence, Assertion (A) is false.

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