CBSE Class 10-Mathematics: Chapter – 6 Triangles Part 18

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Question 2:

Prove that the ratio of areas of two similar triangles are in the ratio of the squares of the corresponding sides. By using the above theorem solve in two similar triangles PQR and LMN, and . Find the ratio of areas of two triangles.

Areas of two similar triangles

Areas of Two Similar Triangles

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Answer:

Given: Two triangles ABC and DEF

Such that

To Prove:

Construction: Draw

Proof:

Again, in we have

Further,

From (ii) and (iii),

Putting in (i), we get

Hence, required ratio is 9:4.