What is a Pythagorean Triple?
-A Pythagorean Triple is 2 square numbers that when added together, equal another square number. The equation for one is:
a² + b² = c²
There are many Pythagorean Triples, but often are confusing to find because when you look at a number squared, like 5², you often ignore or don't see the little ² and end up multiplying by 2 instead of multiplying by 5 again, which is what you should have done. This mistake makes a big difference. 10 is a smaller than 25, and everybody knows that specific math questions have to have an exact answer. A number squared simply means that number times itself. The opposite of squaring is square rooting, which is finding what number times itself equals the larger number.
Anyway, here is my perfect square chart. The highlighted numbers or the ones that are the same color is 1 Pythagorean Triple.
When reading math related word problems, underline important parts and circle the key numbers. Cross out unnecessary or unimportant information, if there is some:
A pictorial version of this problem would be:
The sides are 90 units because, since the measurements of the sides weren't given, you have to go to common sense for help. A square is 360 degrees, meaning it has 4 right angles (90 x 4 = 360). A triangle is half of a square, so it has 180 degrees (90 x 2 = 180) in angle. But we aren't finding the angle of the sides, but the length. So the degrees sign (°) is replaced with units (or u) in place of a measurement.
The new picture of the problem looks like this:
Now we can simply do the equation a² + b² = c² to solve this:
a² + b² = c²
90²+ 90²= c²
√16 200 = √c²
So the missing hypotenuse is 127.27 units in length. You have to throw the ball 127.27 units from first base to third base to get throw the runner out.
Create your own problem:
You are racing down the street on your new 10 speed bike. You see a ramp that 2 of your friend are hauling, and you must jump it to prove you aren't a noob. But your stupid friends are hauling it way further than they are supposed to, 3 meters left of you instead of being straight ahead of you. You are 10 meters away now and must swerve to jump the ramp and end up having to jump at an angle. How many meters do you have to swerve to get to that ramp?
Now, with the key parts highlighted:
Now to answer the question:
What we know:
a = 3 meters
b = 10 meters
c = ?
Here's a little doodle I made on how the problem would look.
Now that we have the numbers, we just do the equations and solve it.
a² + b² = c²
3² + 10² = c²
9 + 100 = c²
109 = c²
√109 = √c²
10 9/21 = c
10 9/11 = 10.42
c = 10.42
So, after solving what the missing side was, you now know that you must swerve 10.42 (closest to 10) meters to the left to jump the ramp. Once you do that, and don't break your neighbors car from jumping onto it, you can retire from your career of dare-deviling and get a nice job as a professional lawn mower.
The End (of Part 4 )