SOLUTION: A triangle has sides which are 9, 40, and 41 millimeters long. How could you determine if this triangle is or is not a right triangle?

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Question 255613: A triangle has sides which are 9, 40, and 41 millimeters long. How could you determine if this triangle is or is not a right triangle?
Found 2 solutions by Alan3354, drk:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest and quickest way is to see if the square of the longest side is the sum of the squares of the other 2 sides.
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9^2 + 40^2 =? 41^2
It is equal, so it's a right triangle.

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We have a thing called the triangle inverse theorem. This has three parts:
If a%5E2+%2B+b%5E2+%3C+c%5E2 then triangle is obtuse
If a%5E2+%2B+b%5E2+=+c%5E2 then triangle is right
If a%5E2+%2B+b%5E2+%3E+c%5E2 then triangle is acute
We also have the triangle inequality statement which says
a+%2B+b+%3E+c
step 1 - apply our numbers to the inequality and we get
9+40 > 41.
So, we have a triangle. Now we put the numbers into the inverse theorem and get
9%5E2+%2B+%2840%5E2%29+__+41%5E2
81+%2B+1600+__+1681
1681+=+1681
This is a right triangle.