if a triangle has side lengths of 6cm, 9cm and x cm, what are possible values for x?
0<x<15cm
x= larger of 0 and lesser of 15cm
10
The lengths of two sides of a triangle are 6 cm and 9 cm. Write all the possible lengths
of the third side
201
1023
To determine the possible values for x in a triangle with side lengths of 6cm, 9cm, and x cm, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have:
Side 1: 6 cm
Side 2: 9 cm
Side 3: x cm
Let's examine the possible combinations using the triangle inequality theorem:
1. Side 1 + Side 2 > Side 3:
6 + 9 > x
15 > x
2. Side 1 + Side 3 > Side 2:
6 + x > 9
x > 3
3. Side 2 + Side 3 > Side 1:
9 + x > 6
x > -3
From the above inequalities, we can conclude that x must be greater than 3 and less than 15. Hence, the possible values for x are 3 < x < 15.