Question

The length of 2 sides of a triangle are 12 inches and 4 inches. Which is the third side?

Answer 1

Answer:

Let x = the third side

 

In a triangle, the sum of any 2 sides must be larger than the third side.

I believe this is called the triangle inequality theorem.

 

We can construct 3 inequalities to obtain the range of values for the third side.

 

  (Inequality #1)   12 + 4 > x

                                  16 > x

 

  (Inequality#2)    12 + x > 4

                                    x > -8   (we can discard this ... we know all sides will be positive)

 

  (Inequality #3)   4 + x > 12

                                   x > 8

 

So when we combine these together,  

 

   8 < x < 16

 

X (the third side) must be a number between 8 and 16. but not including 8 and 16