∆ABC ∼ ∆DEF such that ar(∆ABC) = 36 cm2 and ar(∆DEF) = 49 cm2.

Question:

ABC ∼ ∆DEF such that ar(∆ABC) = 36 cm2 and ar(∆DEF) = 49 cm2.
Then, the ratio of their corresponding sides is
(a) 36 : 49
(b) 6 : 7
(c) 7 : 6

(d) $\sqrt{6}: \sqrt{7}$

 

Solution:

(b) 6:7

"> ∆ABC ∼ ∆DEF

$\therefore \frac{A B}{D E}=\frac{B C}{E F}=\frac{A C}{D F} \quad \ldots(\mathrm{i})$

Also,

$\frac{\operatorname{ar}(\triangle A B C)}{a r(\triangle D E F)}=\frac{A B^{2}}{D E^{2}}$

$\Rightarrow \frac{36}{49}=\frac{A B^{2}}{D E^{2}}$

$\Rightarrow \frac{6}{7}=\frac{A B}{D E}$

$\Rightarrow \frac{A B}{D E}=\frac{B C}{E F}=\frac{A C}{D F}=\frac{6}{7} \quad($ from $(\mathrm{i}))$

Thus, the ratio of corresponding sides is $6: 7$.

 

 

 

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