IPMAT Indore 2024 - QA (SA) Q14 Explanation

Explanation:

(7) 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. Ans

Note: Property of triangle used to eliminate the cases is: Sum of any two sides of a triangle is always greater than the third side.