Triangle inequality practice problems

1. The number of triangles with each side having integral length, and the largest side is of 11 units is equal to \(k^2\), then the value of k is ?.

2. The perimeter of triangle is 20. The length of three sides are all integers. How many triangles are there?

3. A triangle with perimeter 7 has integer side length. What is the maximum possible area of such a triangle?

4. Find the number of isosceles triangles with integral side length and having perimeter 144 and only one side being largest.

5. Find the number of triangles with integral side length such that second largest side is 4 and only one side being largest.


Answers:
Q1 → 6
Q2 → 8
Q3 → \(\frac{3\sqrt{7}}{4}\) unit
Q4 → 11
Q5 → 6

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