Question

sides of two similar triangles are in the ratio 4:9 find the ratio of areas of these triangles​

Answer 1

Step-by-step explanation:

let the triangles be ABC n PQR

ar(ABC)/arPQR=(AB/PQ)whole square.

acc to theorem..

arABC/arPQR=4*4/9*9

Ans-16/81

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Answer 2

Answer:

The ratio of the areas of the triangles is 16 : 81.

Step-by-step explanation:

Given :

Ratio of the sides of the triangle = 4 : 9

The triangles are = Similar triangles

To find :

Ratio of areas of these triangles

Solution :

Corresponding fraction of the ratio of sides of the triangle = $\sf{\dfrac{4}{9}}$

We Know that -

If two triangle are similar,

ratio of areas = ratio of squares of corresponding sides

So,

$\mathsf{ \frac{(Area \: of \: Triangle)_{1}}{(Area \: of \: Triangle)_{2}}} = \mathsf{ \frac{(Side \: of \: Triangle_{1})^{2} }{(Side \: of \: Triangle_{2})^{2}}}$

$\sf{\longrightarrow} \: \left(\dfrac{4}{9}\right)^{2} \\ \\ \sf{\longrightarrow} \: \frac{16}{81} \\ \\ \sf{\longrightarrow} \: 16 : 81$

$\therefore$ The ratio of the areas of the triangles is 16 : 81.