A triangle has two sides mausuring 8.5 cm and 15 CM. What are the least and greatest while number possibilities for the third side?

The least and greatest whole number possibilities for the third side are 7 cm and 23 cm

Solution:

Given that triangle has two sides mausuring 8.5 cm and 15 cm

To find: least and greatest whole number possibilities for the third side

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

By above triangle inequality theorem,

Here the given sides are 8.5 cm and 15 cm, then the inequality becomes:

Let "x" be the length of third side

8.5 + 15 > x

x < 8.5 + 15

x < 23.5

On rounding off we get,

x < 24

Thus the greatest possible whole number for third side is 23 cm

Case 2:

8.5 + x > 15

x > 15 - 8.5

x > 6.5

On rounding off we get,

x > 7

Thus the least possible whole number for third side is 7 cm