Question

दोन समरूप त्रिकोणाच्या क्षेत्रफळाचे गुणोत्तर 144:49 असेल तर त्या त्रिकोणाच्या संगत बाजू चे गुणोत्तर काढा​?​

Answer 1

Given:

दोन समरूप त्रिकोणाच्या क्षेत्रफळाचे गुणोत्तर 144:49 असेल |

To find:

तर त्या त्रिकोणाच्या संगत बाजू चे गुणोत्तर काढा​?​

Solution:

Let the two similar triangles be Δ ABC and Δ PQR.

We know that → "The ratio of the areas of two similar triangles is equal to the square of the ratio of any pair of their corresponding sides".

Considering the above theorem for similar triangles ABC and PQR, we get

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

$\implies \frac{144}{49} = \bigg(\frac{AB}{PQ}\bigg )^2$. . . . [the ratio of areas of the triangles are given as 144:49]

taking square roots on both sides

$\implies \sqrt{\frac{144}{49}} = \bigg(\frac{AB}{PQ}\bigg )$

$\implies \sqrt{\frac{12^2}{7^2}} = \bigg(\frac{AB}{PQ}\bigg )$

$\implies \bold{\bigg(\frac{AB}{PQ}\bigg ) =\frac{12}{7}}$

Thus, the ratio of the corresponding sides of the triangles is → 12 : 7.

________________________________________________

Also View:

If the ratio of areas of similar triangles is 16:121. what is the ratio of their corresponding sides?​

brainly.in/question/28614466

If the ratio of areas of similar triangles are a) 225/81. b) 64/36 c)9/4 find the ratios of their sides.

brainly.in/question/26479421

Answer 2

Given :- If the ratio of the areas of two identical triangles is 144: 49 then what is the ratio of their corresponding sides ?

Solution :-

we know that,

• Ratio of area of two similar ∆'s = Ratio of square of their corresponding sides .

so,

→ Area ∆1 : Area ∆2 = (side 1)² : (side 2)²

→ 144 : 49 = (side 1)² : (side 2)²

→ (12)² : (7)² = (side 1)² : (side 2)²

→ side 1 : side 2 = 12 : 7 (Ans.)

Hence, the ratio of their corresponding sides will be 12 : 7 .

Learn more :-

*जर △ ABC ~ △ DEF असून AB = 12 सेमी and DE = 14 सेमी. तर △ ABC आणि △ DEF यांच्या क्षेत्रफळाचे गुणोत्तर किती?.*

1️⃣ 49/9...

brainly.in/question/37096819

*In triangle ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to …………….*

1️⃣ 7.5 cm

2️⃣ 3 cm

3️⃣ 4.5...

brainly.in/question/37020783

In the figure , Line PQ || Side BC AP = 6 , PB = 8 , AQ = x and QC = 12 , then write the value of x.

brainly.in/question/36586072