Question

1)The ratio of the corresponding sides of similar triangles is 4 : 5, then find ratio of their areas. / दोन समरूप त्रिकोणांच्या संगत बाजूंचे गुणोत्तर 4 : 5 असेल तर त्यांच्या क्षेत्रफळांचे गुणोत्तर काढा. *
2 points​

Answer 1

$\large\bf\underline{To \: Find :—}$

→ We need to find the ratio of areas.

$\large\bf\underline{Given:—}$

→ Ratio of sides of similar triangles is 4:5.

$⚘\huge\bf\underline{Solution:-}$

Let the ratio of sides of two similar triangles be

→ S1 : S2 = 4 : 5

It is given in the Question that the two triangles are similar.

As we know that,

⚘The ratio of areas of two similar triangles is equal to the ratio of square of ratio of two sides.

So,

Let the Ratio of areas of two similar triangles be A1 :A2.

$\rm \dashrightarrow\large \: \frac{A1}{A2} = (\frac{S1}{S2} ) {}^{2}$

$\rm \dashrightarrow\large \: \frac{A1}{A2} = (\frac{4}{5}) {}^{2}$

$\rm \dashrightarrow\large \: \frac{A1}{A2} =( \frac{16}{25}){}$

So,

→ A1 : A2 = 16 : 25

Hence,

❥ Ratio of areas of two similar triangles is 16:25

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