Okay, here's the situation. I just moved to a new house and I need to find the shortest way to work. With the price of gas and other expenses rising, I need to find the most efficient way to save money. I have been trying to figure out how much money I would save in a year (approximately). From my house I drive south 6 miles to the major highway, then I go east 8 miles and finish my traveling at work. Then one day a co-worker told me about another way to get to my house, but he wasn't sure if it was shorter. It seemed to be a more direct route, but we wanted to be sure. The question is "How many miles long is the "new" way"? We can obviously see that the "old" way was 14 miles, but how can we figure out the mileage for the "new" way? Then my next question is how many miles would I save in a year?
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According to the Pythagorean Theorem it says that if we add the squares of the two sides (or legs) and take the square root of the that number, it will give us the distance of the last side (or hypotenuse). First we must realize that the shape formed by the roads is a triangle. Secondly, and really important, is that this a RIGHT TRIANGLE. To get a better understanding click here and follow the instructions on the page.
Okay, do you have a better grasp on what the Pythagorean Theorem is? GOOD. So can you figure out what the mileage is for the "new" way? Let's take a look:
If we Let 6 = one leg of the triangle and Let 8 = the second leg of the triangle we can find the HYPOTENUSE now:
6˛ + 8˛ = HYPOTENUSE˛
36 + 64 = HYPOTENUSE˛
100 = HYPOTENUSE˛
(*** now take the square root of both sides ***)
10 = HYPOTENUSE
Therefore the "new" way is only 10 miles long !!!
NOW, to find how much money I save in year. We will assume 7 days a week and 52 weeks in a year. SO, we have:
WOW !!, now that's a lot of miles, I think I'll take the "new" way for now on.
