Question

Exterior of scalene triangle sides are 25 and 15 and x. solve x.

Answer 1

-- All three sides of a scalene triangle have different lengths.
So 'x' can't be 15 and it can't be 25.

-- 'x' must be 10 or more in order to reach between the ends
of the 25 and the 15.

-- 'x' must be less than 40 in order for the 25 and the 15 to reach
between its ends. 

So the value of 'x' must satisfy these conditions:

0 < x < 15
15 < x < 25
25 < x < 40

Any number that satisfies these conditions is an acceptable value for 'x'.

Answer 2

Let's say we have a triangle with three side lengths.
This triangle is really flat. So much so that you could put it on a number line.
It literally cannot get any flatter, and the largest side literally cannot get any bigger.
Well, the smaller two sides would add <u />up to equal the third.

From this we have realized something: The largest side of any triangle cannot be larger than the sum of the other two.

Let's think back to our problem.
What are the possibilities for $x$?

If $x$ was the biggest side, it couldn't be any bigger than 40.

If $x$ was a smaller side, then that would make 25 the bigger side.
15 and $x$ together can't be any bigger than 25, so $x$ has to be less than 10.

Since it's a scalene triangle, x cannot be 15 or 25 either, so add that too.

$\{x|10\ \textless \ x\ \textless \ 40,\ x\neq15, x\neq25\}$