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# Which inequalities represent the possible lengths for the third side, x?

Two sides of a triangle have lengths 6 and 16. Which inequalities represent the possible lengths for the third side, x?

### 3 Answers by Expert Tutors

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
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let a,b, and c be the lengths of the three sides of a triangle
there are three inequalities:
a+b>c
a+c>b
b+c>a
for your lengths, let a=16 and b=6, therefore a+b>c or 16+6>c; so 22>c or c<22
c can be how much less than 22 ?
look at b+c>a, 6+c>16, c>10
therefore c can be in the following range: 10<c<22
Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
0
Rule for Δ ABC: any two sides added together must be greater than the third side.
If
AB = c
BC = a
AC = b,
then
a + b > c
a + c > b
b + c > a
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If one side of triangle is 6 units, second side is 16 units and third one is "x" units then

x < 16 + 6
x < 22

6 + x > 16
x > 10

10 < x < 22
Daniel R. | PhD student for Math, Science, Computer Science, and EngineeringPhD student for Math, Science, Computer ...
4.9 4.9 (8 lesson ratings) (8)
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The sum of the lengths of any two sides of a triangle must be greater than the third side. Thus, in your case, any length greater than 16+6 = 22 is a valid length for x.