# An obtuse angled triangle has two of its sides #9# and #13#. What is the range for the third side?

##### 1 Answer

Nov 18, 2016

Either

or

#### Explanation:

In an obtuse angled triangle, square on the largest side is greater than sum of the squares on other two sides. However, the largest side is always less than sum of other two sides.

Now, there are two possibilities here.

**(1) - Side with length #13# is longest**

In such a case, we will have

or

and

i.e.

**(2) - Side with length #k# is longest**

In this case, we will have

or

and

i.e.