Two sides of a triangle measure 4cm and 9cm. Determine which of the following choices cannot be the measure of the third side
10cm
8cm
5cm
6cm
To determine which of the given choices cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given sides are 4cm and 9cm. Let x be the measure of the third side.
For x to be a possible third side, it must satisfy the following conditions:
1. 4 + 9 > x
2. 4 + x > 9
3. 9 + x > 4
Let's examine each choice:
1. x = 10cm
4 + 9 > 10 (13 > 10) - True
4 + 10 > 9 (14 > 9) - True
9 + 10 > 4 (19 > 4) - True
2. x = 8cm
4 + 9 > 8 (13 > 8) - True
4 + 8 > 9 (12 > 9) - True
9 + 8 > 4 (17 > 4) - True
3. x = 5cm
4 + 9 > 5 (13 > 5) - True
4 + 5 > 9 (9 > 9) - False
9 + 5 > 4 (14 > 4) - True
4. x = 6cm
4 + 9 > 6 (13 > 6) - True
4 + 6 > 9 (10 > 9) - True
9 + 6 > 4 (15 > 4) - True
Therefore, the third side cannot be 5cm.