If two sides of a triangle have a length of 2ft and 10ft. what are the possible lengths of the Third side?

Question

how do you do it?

Answer 1

It is a pretty simple experiment to get three pencils/straws/etc. and make one of them the base (say, the 10 ft. side), the second one short (for the 2 ft side) and the third for the third side.

 

The rule is:  The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

 

Experiment results:  If the 2 ft side and the third side together are less than or equal to the 10 ft. side, they stay on the line with the 10 ft. side and there is no triangle.  Once their sum is greater than 10 ft., a triangle is formed.

 

This rule applies to each of the three sides.

 

If the sides are 2 ft., 10 ft., and x ft., then:

        2 + 10 > x        that is, 12 > x

        2 + x > 10        that is x > 8

        10 + x > 2        that is x > -8        [this just means that 10 is greater than 2 without the x]

 

Combining these,

                             8 < x < 12             [x must be between 8 and 12]

Answer 2

The sum of any two sides of a triangle is greater than the length of the third.

 

2 + 10 = 12, so the third side has to be less than 12.

 

10 - 2 = 8, so the third side has to be greater than 8.

 

Hope this helps.