If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range
Practice Questions
Q1
If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of possible lengths for the third side?
1 cm to 17 cm
6 cm to 16 cm
7 cm to 12 cm
5 cm to 12 cm
Questions & Step-by-Step Solutions
If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of possible lengths for the third side?
Step 1: Identify the lengths of the two sides of the triangle. Here, they are 5 cm and 12 cm.
Step 2: Calculate the difference between the two sides. This is |5 - 12| = 7 cm.
Step 3: Calculate the sum of the two sides. This is 5 + 12 = 17 cm.
Step 4: The length of the third side must be greater than the difference (7 cm) and less than the sum (17 cm).
Step 5: Write the range for the third side: 7 cm < third side < 17 cm.
Triangle Inequality Theorem – The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
