# GEOM 2| Lesson 1 | Explore Solutions

While explore the three numbers, here are some that work:

$$(3, 4, 5)$$, $$(3, 4, 6)$$, $$(3, 5, 6)$$, $$(3, 6, 8)$$, $$(3, 8, 10)$$

$$(4, 5, 6)$$, $$(4, 5, 8)$$, $$(4, 6, 8)$$, $$(4, 8, 10)$$

$$(5, 6, 8)$$, $$(5, 6, 10)$$, $$(5, 8, 10)$$, $$(6, 8, 10)$$

Did you find any others that work?

You should notice that the sum of the lengths of any two sides must be greater than the length of the third side.

If a, b, and c are lengths of the sides of the triangle then $$a + b > c$$, $$a + c > b$$ and $$b + c > a$$.

1.   yes
2.   no
3.   no
4.   yes