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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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Similar Questions

  1. What is the area of quadrilateral ABCD?

  2. AD is the median of the triangle ABC. If P is any point on AD, then which one of the following is correct?

  3. In a triangle ABC, if 2 ∠A = 3 ∠B = 6 ∠C, then what is ∠A + ∠C equal to?

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  5. ABC is an equilateral triangle. The side BC is trisected at D such that BC = 3 BD. What is the ratio of AD 2to AB 2?

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  7. If ABC is a right-angled triangle with AC as its hypotenuse, then which one of the following is 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:

  2. If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?

  3. What is the area of quadrilateral ABCD?

  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)?

  5. Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:

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