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# Triangle Inequality

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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?

Jan 15, 2024

#1
+293
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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?

Well, we know that 2 sides of the triangle are the same, since it is iscoceles. that means that the 2 sides can either be 2 or 1. But, we can rule out 1, since 2 sides of a triangle musts add up to be more than the 3rd side, but if the iscoceles sides are each 1, then 1+1<3, so that is not true. That leaves only one option, which is that iscoceles sides are 2, and the other side is 1.

Jan 15, 2024

#1
+293
+1

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?

Well, we know that 2 sides of the triangle are the same, since it is iscoceles. that means that the 2 sides can either be 2 or 1. But, we can rule out 1, since 2 sides of a triangle musts add up to be more than the 3rd side, but if the iscoceles sides are each 1, then 1+1<3, so that is not true. That leaves only one option, which is that iscoceles sides are 2, and the other side is 1.

Imcool Jan 15, 2024