Question

A triangle has two sides of lengths 7 and 12. What value could the length of

the third side be?
Check all that apply.
A. 7
B. 9
C. 17
D. 3
E. 5
F. 11

Answer 1

To determine what value the length of the third side of the triangle could be, we need to use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's call the length of the third side x. Then, we can write two inequalities based on the given information:

7 + 12 > x
x + 7 > 12

Simplifying the second inequality, we get:

x > 5

Therefore, the possible values for the length of the third side are:

B. 9
C. 17
E. 5
F. 11

These values satisfy both inequalities and are consistent with the triangle inequality theorem.

A and D are not possible because 7 - 12 = -5, which is not greater than 0 and violates the triangle inequality theorem.