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Question

If two similar scalene triangles ABC and PQR have the same area, then which of the following statements is/are correct?

I. Both the triangles are congruent.

II. Both the triangles have equal perimeters.

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This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

Both I and II

For similar triangles ABC and PQR with similarity ratio k, the ratio of their areas is \(k^2\). If the areas are equal, \(k^2 = 1 \Rightarrow k = 1\), so all corresponding sides are equal and the triangles are congruent (Statement I true). Since the perimeter also scales by the same factor k, k = 1 also makes the perimeters equal (Statement II true). Hence both statements are correct.

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Important Questions from Triangles, Congruence and Similarity

  1. G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:

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  4. It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?

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