Question

Two sides of a triangle mesure 20cm and 30cm. What is the measure of the third side

Answer 1

All real numbers greater than
`10\ cm` and less than
`50\ cm`

Explanation:

we know that

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

Let

c-----> the length of the third side

Applying the theorem

case A)

`20+30> c\\50> c\\ c< 50\ cm`

case B)

`20+c > 30\\c > 30-20\\c> 10\ cm`

The solution for the measure of the third side of the triangle is the interval

`(10,50)`

All real numbers greater than
`10\ cm` and less than
`50\ cm`