What devastating historic event compelled many european countries to work together in order to prevent future conflicts?

There are two examples. 1. World war 1. In which case, many countries formed a league in order to prevent such an event from happening again. The league is called the "League of Nations" which composed of many European countries but it was ineffective because of the little military backing it had because the U.S did NOT join the organization. Another example would be World war 2 in which became the deadliest and most causality rated war in history.  Over 50 million people died. After the war, the United States became the leader of the free world and helped form the United Nations which is composed of about 193 nations out of 196-198 nations in the world. The League of nations disbanded and the United Nations took its place and still exists today as a peacekeeping organization.

the answer would be the third option, "no, ariel should have added 9^2 and 12^2 and compared that to 15^2."

this is found through the pythagorean theorem, which is a^2 + b^2 = c^2.

this is the correct way of solving the problem:

9^2 + 12^2 = 15^2

81 + 144 = 225

225 = 225