If a triangle has sides of lengths 5 and 13, then the possible lengths of the third side are __________.

Question

If a triangle has sides of lengths 5 and 13, then the possible lengths of the third side are __________. 

 

 

a	11 < x < 13
b	8 < x < 18
c	2 < x < 24
d	5 < x < 13

Answer 1

Sum of lengths of any side of a triangle must be less than the combined length of the other two sides.

For triangle with sides 5 and 13, other side must be less than 5 + 13 = 18

and other side must be greater than 13-5 = 8, so 8 < x < 18 (b)

Answer 2

x < 5 + 13 = 18, x < 18 and x > 13 - 5 = 8, x > 8.

So, 8 < x < 18. We use triangle inequality.

Answer is b: 8 < x < 18