Step by step
The question
Question: can sides of 4, 6 and 10 make a triangle?
sides 4, 6, 10
For a triangle, the two short sides together must be longer than the longest side.
Else they cannot meet.
the two short sides must reach
round the longest one
1 Add the two short sides
The longest side is 10.
We lay it down first.
The two short sides are 4 and 6.
Together: 10.
= 4 + 6 = 10
2 Compare with the longest
Swing them up from the ends.
10 is exactly 10: they only meet lying flat on the long side.
Careful!
4 plus 6 is exactly 10.
The sides lie flat on top of each other.
That is a line, not a triangle.
Careful: equal is not enough: it lies flat
So no: they cannot make a triangle.
= 10 = 10 → no triangle
3 Check
Let's check the other two pairs: 4 plus 10 is 14, and 6 plus 10 is 16.
Both are more than the third side.
So only the short pair decides.
So the answer is right!
4 + 10 = 14 > 6, 6 + 10 = 16 > 4
Let's look back.
First: add the two short sides.
Then: compare with the longest.
Last: check.
Answer
= 10 = 10 → no triangle