Question

Do these measurements create a triangle? true or false?

Answer 1

Question 9: False

Question 10: False

Explanation:

The third side is always greater than the other two sides.

Question 9

a = 6, b = 6, c = 5

Since the third side is the smallest, it would not create a triangle.

Question 10

a = 7, b = 2, c = 5

Since the third side is the smallest, it would not create a triangle.

Answer 2

Question 9: True

Question 10: False

Explanation:

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the last side.

To test if the three lengths create a triangle you would have to test the three combinations if the two numbers are greater than the last number.

Question 9:

The three lengths 6, 6, 5 create a triangle.

First check the first two numbers.

• 6 + 6 = 12
• 12 > 5, so this is valid.

Next check the first and last number.

• 6 + 5 = 11
• 11 > 6, this is also valid.

Last check the second and last number.

• 6 + 5 = 11
• 11 > 6, all three combinations are valid for creating a triangle.

The answer for question 9 is TRUE.

Question 10:

The three lengths 7, 2, 5 create a triangle.

Check the first two numbers.

• 7 + 2 = 9
• 9 > 5, this is valid.

Check the first and last number.

• 7 + 5 = 12
• 12 > 2, this is also valid.

Finally, check the second and last number.

• 2 + 5 = 7
• 7 = 7, this is NOT valid because it MUST be greater than. Therefore these three lengths are not able to create a triangle.

The answer for question 10 is FALSE.