In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
Practice Questions
1 question
Q1
In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
3 cm
15 cm
5 cm
17 cm
According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
Solution: According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.
Steps: 5
Step 1: Identify the lengths of the two sides of the triangle. Here, they are 7 cm and 10 cm.
Step 2: Use the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides.
Step 3: Calculate the sum of the two sides: 7 cm + 10 cm = 17 cm. This means the third side must be less than 17 cm.
Step 4: Calculate the difference of the two sides: 10 cm - 7 cm = 3 cm. This means the third side must be greater than 3 cm.
Step 5: Combine the results from Steps 3 and 4. The length of the third side must be greater than 3 cm and less than 17 cm.
