Question

दोन समरूप त्रिकोणाच्या संगत बाजूंचे गुणोत्तर 5:7 आहे तर त्यांच्या क्षेत्रफळाचे गुणोत्तर किती?​

Answer 1

Given:

दोन समरूप त्रिकोणाच्या संगत बाजूंचे गुणोत्तर 5:7 आहे तर त्यांच्या क्षेत्रफळाचे गुणोत्तर किती?​

If the ratio of the corresponding sides of two identical triangles is 5 : 7, what is the ratio of their areas?

To find:

What is the ratio of their areas?

Solution:

Let's say ABC and PQR are two similar triangles, so

"5x" → the length of side AB

"7x" → the length of side PQ

We know,

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

Based on the above theorem, we get

$\frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \bigg(\frac{AB^2}{PQ^2} \bigg)$

$\implies \frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \bigg(\frac{AB}{PQ} \bigg)^2$

on substituting the values of AB = 5x and PQ = 7x, we get

$\implies \frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \bigg(\frac{5x}{7x} \bigg)^2$

$\implies \frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \frac{25x^2}{49x^2}$

$\implies\bold{ \frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \frac{25}{49}}$  

 

  Thus, the ratio of their areas is → 25:49.

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Also View:

Find the ratio of the areas of two similar triangles if two of their corresponding sides are of length 3 cm and 5 cm.

brainly.in/question/11234579

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

brainly.in/question/5207774?tbs_match=2

Answer 2

Answer:

25:49

Step-by-step explanation:

this is mcq type question so no explanation