Question

A triangle has two sides of lengths 4 and 7. What value could the length of the third side be? Check all that apply.

A. 5
B. 11
C. 17
D. 7
E. 3
F. 9

Answer 1

The possible values for the length of the third side of the triangle are 5, 7, and 9. Hence the correct answer is option A , D and F

Step-by-step explanation:

To find the possible values for the length of the third side of a triangle with two sides of lengths 4 and 7, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, in our case, the length of the third side must be less than the sum of 4 and 7, and greater than the difference between 7 and 4.

Therefore, the length of the third side must be greater than 3 (7 - 4) and less than 11 (4 + 7).

From the given options, the values that satisfy this condition are:

• 5
• 7
• 9

Hence the correct answer is option A , D and F