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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
One equilateral triangle with sides (5, 5, 5)
Three isosceles triangles (7, 7, 1), (6, 6, 3) and (4, 4, 7)
Reason: The measure of two equal sides cannot be less than 4 or more than 7. Taking two equal sides as 8 will make sum of these two sides only as 16, more than the perimeter. Taking two equal sides as 3 each, the third side will be 9, eventually not following the property of triangle.
Three scalene triangles (7, 6, 2), (7, 5, 3), (6, 5, 4)
Reason: The maximum measure of two equal sides of the triangle can be 7 or 6 only. Taking 8 as the largest side of the triangle will leave us with the sum of other two sides as 7. Taking 5 as the largest side of triangle we end up getting an equilateral triangle which we have already considered before. 4 cannot be the largest side.
Total number of possible triangles is 7.