The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of a triangle are 16 ft and 21 ft. Find the possible lengths of the third side?

Question

The third side must have a length greater than blank ft and less than blank ft

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Answer 1 · 2018-02-24T03:45:29

The third side must have a length greater than, but not including, #5# feet and less than, but not including, #37# feet, i.e. #5<c<37#.

Say the three sides of the triangle are #a,b# and #c#. Here, #a=16# and #b=21#. We must find the possible values of #c#.

Since #a+c>b#, we can input:

#16+c>21#

#c>5#.

So the lower bound of #c# is everything above #5#.

We also know that #a+b>c#. Inputting:

#16+21>c #

#37>c#.

So #c# must be less than, but not including #37#.

In conclusion, the side length #c# must satisfy the following inequality:

#5<c<37#