Question

Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 8 and 13

Answer 1

5 < third side < 21

Explanation:

Let the length of the third side be
`x`.

We know that
`x` must be smaller than the sum of the lengths of the two other sides. Thus
`x < 21`.

We also know that

`x+8 > 13\\x > 5`

And

`x+13 > 8\\x > -5`

So, in conclusion,
`5 < x < 21`.