Question

Find the range for the possible measure of the third side of a triangle given two sides?

4 cm, 6 cm
Range:

Answer 1

The possible range of the measure of the third side is 2 < 3rd side < 10

Explanation:

In any triangle:

• The sum of the lengths of any two sides must be greater than the length of the 3rd side

• The length of any side must greater than the difference of the lengths of the other two sides

• The difference of the other sides < The side < The sum of the other sides

Let us solve the question

∵ The measures of the two sides of a triangle are 4 cm and 6 cm

∵ The difference between their measures = 6 - 4 = 2 cm

∵ The sum of their measures = 6 + 4 = 10 cm

→ By using the rules above

∴ The measure of the third side is between 2 and 10

∴ 2 < the third side < 10

∴ The possible range of the measure of the third side is 2 < 3rd side < 10