Question

Is it possible to draw a triangle whose sides are of the following lengths (all in cm)? Give reason.

4.2, 6, 1.7

Answer 1

To determine if a triangle can be formed with sides of lengths 4.2 cm, 6 cm and 1.7 cm, we again apply the triangle inequality theorem. According to this theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let’s check the three conditions:

4.2 + 6 > 1.7
10.2 > 1.7 (True)

4.2 + 1.7 > 6
5.9 > 6 (False)

6 + 1.7 > 4.2
7.7 > 4.2 (True)

Since the second condition fails, a triangle with sides of lengths 4.2 cm, 6 cm and 1.7 cm cannot be formed.

Therefore, the answer is No, a triangle with these side lengths is not possible.