Question

The measures of two sides of a triangle are 8 and 15, what is the range possible values for the third side?

Answer 1

The required range is
`7<C<23`.

Explanation:

Consider the provided information.

Let the side A = 15 and the side B = 8

Theorem 1: For a triangle with sides A, B, and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

`A+B>C` ....(1)

`B+C>A` ...(2)

`A+C>B` ....(3)

By using equations 1 and 2.

Therefore,
`A-B<C<A+B`

`15-8<C<15+8`

`7<C<123`

Hence, the required range is
`7<C<23`.