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. 13

b. 5

c. 22

d. 10

e. 8

f. 2

Answer 1

The length of the third side of a triangle with sides of lengths 7 and 9 could be 5, 8, 10, or 13.

Step-by-step explanation:

A triangle can be formed with sides of lengths 7, 9, and a third side. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the length of the third side must be greater than the absolute value of the difference between the lengths of the two known sides and less than the sum of their lengths.

In this case, the difference between the lengths of the two known sides is |7-9| = 2, and the sum of their lengths is 7+9 = 16. So, the length of the third side must be greater than 2 and less than 16.

Therefore, the possible values for the length of the third side are 5, 8, 10, and 13.