Question

By the Triangle Inequality Theorem, if two sides of a triangle have lengths of 6 and 13, what are the possible lengths of the third side?

Answer 1

a= 6 b=13   ∴    29>c
                         29+a > b
                          29>b-a     
therefore      b-a < c 
                        5<c< 29
                      

Answer 2

The possible lengths of third side are 8, 9, 10, 11, 12, 13, 14, 15, 16,17, 18 cm.

Triangle inequalities

Sum of two sides is greater than the third side.

Difference of two sides is less than the third side.

Given sides 6 & 13 cm

Let the third side be x cm

Sum inequality :

6 + 13 > x

19 > x

Difference inequality :

13 - 6 < x

7 < x.

Therefore, The third side lies in the range (7,19)

If third side is x, then 7 < x < 19