Question

A triangle has two sides of lengths 7 and 9. What value could the length of

the third side be? Check all that apply.
☐A. 10
B. 2
C. 8
OD. 5
E. 13
OF. 22

Answer 1

To determine the possible lengths of the third side of a triangle with sides of lengths 7 and 9, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check the options:

A. 10: 7 + 9 > 10 (True)
B. 2: 2 + 7 > 9 (True)
C. 8: 7 + 8 > 9 (True)
OD. 5: 5 + 7 > 9 (True)
E. 13: 7 + 9 > 13 (True)
OF. 22: 7 + 22 > 9 (True)

From the checks above, all options except for B (2) and OF (22) satisfy the triangle inequality theorem and could be valid lengths for the third side of the triangle. Therefore, the correct answers are:

☐A. 10
☐C. 8
☐OD. 5
☐E. 13