Question

Sides of two similar triangle are in the ratio 4:9areas of these triangle are in the ratio

Answer 1

GivEn:-

• Ratio of sides of two triangles is 4:9.

To find:-

• Ratio of there area.

SoluTion:-

As we know that,

If two triangles are similar to each other, then the ratio of the areas of these triangle will be equal to the square of the ratio of the corresponding sides of these triangles.

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GivEn that,

Ratio of there sides = 4:9

$\therefore$ Ratio b/w the areas of these triangles :-

☯ Squaring the given ratio of sides :-

$\dashrightarrow\sf \bigg( \dfrac{4}{9} \bigg)^2 = \dfrac{16}{81}$

$\dag$ Hence, ${\bf{\blue{16:81}}}$ is the ratio of areas of these triangles.

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Answer 2

Given ,

The ratio of sides of two similar triangles is 4 : 9

We know that ,

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides

Thus ,

$\sf \mapsto \frac{Area \: of \: first \: triangle }{Area \: of \: second \: triangle} = { (\frac{4}{9} )}^{2} \\ \\\sf \mapsto \frac{Area \: of \: first \: triangle }{Area \: of \: second \: triangle} = \frac{16}{81}$

$\sf \therefore\underline{The \: ratio \: of \: the \: areas \: of \: given \: two \: similar \: triangles \: is \: \frac{16}{81} }$