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?

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) (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.
--------
9^2 + 40^2 =? 41^2
It is equal, so it's a right triangle.

Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We have a thing called the triangle inverse theorem. This has three parts:
If then triangle is obtuse
If then triangle is right
If then triangle is acute
We also have the triangle inequality statement which says

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

This is a right triangle.
RELATED QUESTIONS
A triangle has sides which are 9, 40, and 41 centimeters long. what is the area? (answered by KMST)
if a triangle has sides 9,40, and 41 is it a right triangle? (answered by swincher4391)
A triangle has a perimeter of 44.4 millimeters. Two of the sides measure 14.8 millimeters (answered by Alan3354,macston)
A triangle has a perimeter of 72 millimeters. Two of the sides measure 18 millimeters and (answered by Alan3354,fractalier)
A triangle has sides of squareroot of 2 and 3. Which could not be the length of the... (answered by stanbon)
A triangle has sides of and 3. Which could not be the length of the third side if it is... (answered by checkley77)
A Triancle is Isosceles if it has at least two sides that are congruent. if the vertices... (answered by Alan3354)
Hi. I'm wondering if I am on the righ track with this one.. In triangle ABC we have... (answered by scott8148)
If one has the measurement of the three sides of a triangle, how can one determine if the (answered by vleith)