$I f △ A B C \sim△ D E F s u c h t h a t A B = 6 c m a n d D E = 7 c m . F i n d t h e r a t i o o f a r e a s o f △ A B C a n d △ D E F .$

49/36

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3/12

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36/49

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6/7

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Solution

The correct option is C
36/49

$W e k n o w t h a t t h e r a t i o o f a r e a s o f t w o s i m i l a r t r i a n g l e s i s e q u a l t o t h e r a t i o o f t h e s q u a r e s o f a n y t w o c o r r e s p o n d i n g s i d e s . ∴ \frac{A r e a (△ A B C)}{A r e a (△ D E F)} = \frac{A B^{2}}{D E^{2}} \Rightarrow \frac{A r e a (△ A B C)}{A r e a (△ D E F)} = \frac{(6)^{2}}{(7)^{2}} = {(\frac{6}{7})}^{2} = \frac{36}{49}$

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