Suppose you had a big triangle ABC, maybe meters instead of centimeters,
drawn on the ground.
1. If you start at A, walk from A to B and then from B to C,
then you must have walked farther than if you had walked
directly along the straight line from A to C.
2. If you start at B, walk from B to C then from C to A,
then you must have walked farther than if you had walked
directly along the straight line from B to A.
3. If you start at C, walk from C to A and then from A to B,
then you must have walked farther than if you had walked
directly along the straight line from C to A.
Why is this? Becuas the shortest distance between any two
points and must be shorter than any other path.
So let the third stick be x cm long.
Then the sides of the triangle are x, 5, and 9 cm.
The sum of any two must be greater than the third, so we havd the three inequalities
x+5 > 9, x+9 > 5 and 5+9 > x
x > 4 x > -4 14 > x
The middle one is obvious. The other two give us:
4 < x < 14, so the third side must be more than 4 cm and
less than 14 cm.
Edwin
