Question

For a triangle with sides a, b and c, what is the range of the length of side c?
a = 418, b = 222, c =
___________ < c < __________

Answer 1

Because of the triangle inequality thm, which says that two sides of a triangle must ALWAYS add up to longer than the third side, there are restrictions on the length of the third side of a triangle. Here's why:


This is a situation where the two sides are smaller than the third. It can't close the figure!

Here's a situation where it's the same size. They're just two lines right on top of each other, not a triangle.

So the sum of two sides must always be greater than the third.

If two sides a = 418 and b = 222 are sides of a triangle, then:
a + b > c
b + c > a
a + c > b

Plugging our values in,
418 + 222 > c
c < 640
222 + c > 418
c > 196
418 + c > 222
c > -196

196 < c < 640