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All the sides of a triangle have integer length. The perimeter of the triangle is 5 and the triangle is isosceles. How many such non-congruent triangles are there?

 Mar 5, 2024
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Set the side lengths of the triangle to be \(x, x, y\)

\(2x+y=5\), so \(2x<5\) and \(x\le2\).

Therefore, because x is a positive integer, x is either 1 or 2.

But we need to be careful because 1, 1, 3 is not a triangle.

So the only possibility is 2, 2, 1.

 Mar 6, 2024

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