Question

9.Ratio of corresponding sides of two similar triangles is 4:7 then find the ratio of

their areas = ?​

Answer 1

The ratio of areas of similar triangles is equal to the square of the ratio of their corresponding sides. ( it is a theorem... for proof refer NCERT class 10 :) )

$\frac{area \: triangle \: 1}{area \: triangle \: 2} = \frac{ {4}^{2} }{ {7}^{2} } \\ = > \frac{area \: triangle \: 1}{area \: triangle \: 2} = \frac{16}{49}$

there you go :)

Answer 2

Answer:

Given:-

• Ratio of corresponding sides of two similar triangles is 4:7.

To Find:-

• Ratio of their areas

Theorem Used:-

• The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. ____ {1}

Solution:-

Let the corresponding sides of similar triangles be $S_{1} and S_{2}$ and their corresponding areas be $A_{1} \:and\: A_{2}$.

As Given,

⇒ $S_{1} : S_{2}$ = 4 : 7

So,

⇒ $\dfrac{S_1}{S_2}\: = \: \dfrac{4}{7}$ ____ {2}

From {1} we get,

⇒ $\dfrac{A_1}{A_2}\: = \: \dfrac{S_{1}²}{S_{2}²}$

= $(\dfrac{S_{1}}{S_{2}})²$

From {2} we get,

= $(\dfrac{4}{7})²$

= $\dfrac{16}{49}$

Hence, the ratio of areas of similar triangles is 16:49.

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