If the altitudes of a triangle are in the ratio $2 : 3 : 4$ , then the lengths of the corresponding sides are in the ratio

2 : 3 : 4

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6 : 4 : 3

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3 : 2 : 4

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3 : 2 : 1

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Solution

The correct option is B $6 : 4 : 3$
$G i v e n : △ A B C, A D, B E a n d C F a r e a l t i t u d e s d r a w n o n t h e s i d e s B C, C A a n d A B r e s p e c t i v e l y A D : B E : C F = 2 : 3 : 4 L e t A D = 2 x, B E = 3 x, C F = 4 x A r e a o f △ A B C = \frac{1}{2} \times B C \times A D = \frac{1}{2} \times C A \times B E = \frac{1}{2} \times A B \times C F \Rightarrow B C \times A D = C A \times B E = A B \times C F \Rightarrow 2 x B C = 3 x C A = 4 x A B \Rightarrow 2 B C = 3 C A = 4 A B \Rightarrow \frac{B C}{6} = \frac{C A}{4} = \frac{A B}{3} [D i v i d i n g b y 12] \Rightarrow A B : B C : C A = 6 : 4 : 3 H e n c e o p t i o n (B) i s c o r r e c t a n s w e r$

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The areas of two similar triangles are $9 c m^{2} a n d 16 c m^{2}$ respectively . The ratio of their corresponding sides is ____.

4 : 5 : 6

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