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The ratio for the side lengths of a right triangle is 3:4:5. If the perimeter is 48, what is the area of the triangle?

"Interpreting the Copernican Revolution" by Matthew Minerd (2014) The expressions of one discipline can often alter the way that other subjects understand themselves. Among such cases are numbered the investigations of Nicolaus Copernicus. Copernicus is best known for his views concerning heliocentrism, a view which eventually obliterated many aspects of the ancient/medieval worldview, at least from the standpoint of physical science. It had always been the natural view of mankind that the earth stood at the center of the universe, a fixed point in reference to the rest of the visible bodies. The sun, stars, and planets all rotated around the earth. With time, this viewpoint became one of the major reference points for modern life. It provided a provocative image that was used – and often abused – by many people for various purposes. For those who wished to weaken the control of religion on mankind, it was said that the heliocentric outlook proved man’s insignificance. In contrast with earlier geocentrism, heliocentrism was said to show that man is not the center of the universe. He is merely one small being in the midst of a large cosmos. However, others wished to use the “Copernican Revolution” in a very different manner. These thinkers wanted to show that there was another “recentering” that had to happen. Once upon a time, we talked about the world. Now, however, it was necessary to talk of man as the central reference point. Just as the solar system was “centered” on the sun, so too should the sciences be centered on the human person. However, both of these approaches are fraught with problems. Those who wished to undermine the religious mindset rather misunderstood the former outlook on the solar system. The earlier geocentric mindset did not believe that the earth was the most important body in the heavens. Instead, many ancient and medieval thinkers believed that the highest “sphere” above the earth was the most important being in the physical universe. Likewise, the so-called “Copernican Revolution” in physics was different from the one applied to the human person. Copernicus’ revolution showed that the human point of view was not the center, whereas the later forms of “Copernican revolution” wished to show just the opposite. Of course, there are many complexities in the history of such important changes in scientific outlook. Nevertheless, it is fascinating to see the wide-reaching effects of such discoveries, even when they have numerous, ambiguous effects. What can we say of the effects of Copernicus’ discoveries on the reigning medieval way of looking at the world?

Solve: 0.25 + 0.65

If 11 + 3x is 29, what is 2x?