Question

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

6.5, 3.2, 9.7

Answer 1

To determine if a triangle can be formed with side lengths of 6.5 cm, 3.2 cm and 9.7 cm, we need to apply the triangle inequality theorem. This theorem states that 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:

6.5 + 3.2 > 9.7
9.7 > 9.7 (False)

6.5 + 9.7 > 3.2
16.2 > 3.2 (True)

3.2 + 9.7 > 6.5
12.9 > 6.5 (True)

Since the first condition fails, a triangle with side lengths of 6.5 cm, 3.2 cm and 9.7 cm cannot be formed.

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