Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order. pick three numbers
According to the Triangle Inequality Theorem, the sum of the two smaller sides of a triangle must be greater than the third side.
If the first two sides measure 6 and 2, then the possible whole number measures of the third side must satisfy the inequalities:
1. 6 + 2 > x
2. 6 + x > 2
3. 2 + x > 6
Solving these inequalities gives the possible solutions for x:
1. 6 + 2 > x --> 8 > x
2. 6 + x > 2 --> x > -4
3. 2 + x > 6 --> x > 4
Combining these three conditions, we find that x must be greater than 4 and less than 8. The whole number values within this range are 5, 6, and 7.
Therefore, the possible whole number measures of the third side are 5, 6, and 7.