A triangle has two sides of length 5 and 12. What value could the length of the third side be? Check all that apply.

A. 19
B. 7
C. 9
D. 5
E. 17
F. 11

Question

A triangle has two sides of length 5 and 12. What value could the length of the third side be? Check all that apply.

 		A.	19
 		B.	7
 		C.	9
 		D.	5
 		E.	17
 		F.	11

anonymous · Answer

helpp mee

mathstudent55 · Answer

For a triangle with two side lengths a and b, the length of the third side, c,  must be between a - b and a + b. As an inequality, this is expressed as
a - b < c < a + b

mathstudent55 · Answer

In other words, if you are given the lengths of two sides of a triangle and you want to know what length the third side can be, add the two lengths and subtract the two legths. The third side's length is in between the two numbers.

anonymous · Answer

all the numbers inbetween?

mathstudent55 · Answer

Right.
In this case, 12 - 5 = 7; 12 + 5 = 17.
The third side can be anything between 7 and 17, but not 7 and 17 themselves.