Math Problems, Probability Problems

Problem of the Day: 1/8/13

In how many distinct ways can the letters of the word ALGEBRA be arranged?

Solution to yesterday’s problem:
Let’s show the diagram again, with a few small changes:

As you can see, I’ve created two 30-60-90 right triangles (the angle between two sides of a regular hexagon is always 120°). Along with this, you should remember that if the short side is a, the hypotenuse is 2a and the long side is a\sqrt{2}.

Knowing these facts about 30-60-90 triangles, let’s find a. The hypotenuse is 6 inches at 2a, so the short side must be 3 inches. Then, the long side is 3\sqrt{2} inches long. With two of these long sides put together, the total side length of the square is 6\sqrt{2} inches.

To find the area of the square, we square this side length to get 36 \times 2, or 72 square inches.


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