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

1 Answer

Solution :-

Right answer is (D) 16 : 81

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

Triangles Exercise 6.4 Answer 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

Related Questions

In an trapezium ABCD, it is given that AB ∥ CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(∆AOB) = 84 cm2. Find ar(∆COD)

Class 10 Maths Triangles View Answer

Find the length of the altitude of an equilateral triangle of side 2a cm.

Class 10 Maths Triangles View Answer

A ladder 10 m long reaches the window of a house 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Class 10 Maths Triangles View Answer

In the given figure, DE ∥ BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.

Class 10 Maths Triangles View Answer

If ∆ABC ∼ ∆DEF such that 2 AB = DE and BC = 6 cm, find EF.

Class 10 Maths Triangles View Answer