Answer :
-- 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'.
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 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 [tex]x[/tex]?
If [tex]x[/tex] was the biggest side, it couldn't be any bigger than 40.
If [tex]x[/tex] was a smaller side, then that would make 25 the bigger side.
15 and [tex]x[/tex] together can't be any bigger than 25, so [tex]x[/tex] has to be less than 10.
Since it's a scalene triangle, x cannot be 15 or 25 either, so add that too.
[tex]\{x|10\ \textless \ x\ \textless \ 40,\ x\neq15, x\neq25\}[/tex]
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 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 [tex]x[/tex]?
If [tex]x[/tex] was the biggest side, it couldn't be any bigger than 40.
If [tex]x[/tex] was a smaller side, then that would make 25 the bigger side.
15 and [tex]x[/tex] together can't be any bigger than 25, so [tex]x[/tex] has to be less than 10.
Since it's a scalene triangle, x cannot be 15 or 25 either, so add that too.
[tex]\{x|10\ \textless \ x\ \textless \ 40,\ x\neq15, x\neq25\}[/tex]
