Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

(A) 2 : 3

(B) 4 : 9

(C) 81 : 16

(D) 16 : 81

Asked by Pragya Singh | 1 year ago |  38

##### Solution :-

Right answer is (D) 16 : 81

Given, Sides of two similar triangles are in the ratio 4 : 9.

Let ABC and DEF are two similar triangles, such that,

ΔABC ~ ΔDEF

And $$\dfrac{AB}{DE}$$$$\dfrac{AC}{DF}$$$$\dfrac{BC}{EF}$$$$\dfrac{4}{9}$$

As, the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides,

$$\dfrac{ Area(ΔABC)}{Area(ΔDEF)}$$ = $$\dfrac{AB^2}{DE^2}$$

$$\dfrac{ Area(ΔABC)}{Area(ΔDEF)}$$ = ($$\dfrac{4}{9}$$)$$\dfrac{16}{81}$$ = 16:81

Answered by Abhisek | 1 year ago

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