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