Question

The perimeter of a triangle is 12 cm. Ifall the three sides have lengths (incm), in integers, then how many suchdifferent triangles are possible ?​

Answer 1

The perimeter of a triangle is 12 cm. If all the three sides have lengths (incm), in integers, then 3 different triangles are possible

According to the triangle inequality theorem, it states that, the sum of any 2 sides should be greater than the third side.

So, for a triangle of perimeter = 12 cm, we can see that the following sets satisfy the triangle inequality theorem:

1) (3,4,5)            [3+4>5]

Sides are 3cm, 4cm, 5cm.

2) (2,5,5)           [2+5>5]

Sides are 2cm, 5cm, 5cm.

3) (4,4,4)            [4+4>4]

Sides are 4cm, 4cm, 4cm.

So, we can construct three different triangles by satisfying the inequality theorem.