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. Select the answer using the code given below:
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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