What could be the possible third length of a triangle with two given side lengths of 7 and 13?

Question

I dont understand this question at all.....

Answer 1

It really helps to see a picture when trying to understand this problem.  If possible, cut narrow strips of paper with 7 lines and 13 lines from your notebook paper.  Connect one end of each; then imagine a third side of a triangle.  What could be it's length?

 

The important concept is that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.  [the three sides don't form a triangle if this is not true]

 

With two sides of a=7 and b=13, side c must be greater than 6 (because 7+6=13).

 

But, don't forget that 7 + 13 (that is a+b) must be greater than c.  Thus:  20 > c.

 

This means, combining these, that:    6 < c < 20       [THX to Arthur for correction]

Answer 2

the sum of the lengths of any two sides of a triangle must be greater than the length of the third side

let a, b, and c be the lengths of the triangle

a+b>c

a+c>b

b+c>a

these all must be true

let a=13 and b=7

what can c possibly be ??

look at b+c>a

7+c>13

c>13-7

c>6

the length of c can be any number greater than 6

the length of c cannot be 6 or less than 6 because 6+7 is not greater than 13

6.1 will work, 6.2 will work, 6.01 will work, and so on

you probably want whole numbers so c must be 7 or 8 or 9 or ... or 19