Question 1176696: A triangle has sides with lengths of 4 centimeters, 9 centimeters, and 12 centimeters. Is it a right triangle?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Rule: If we have a triangle of sides a,b,c such that c is the longest side and a^2+b^2 = c^2 is a true equation, then this triangle is a right triangle. This is the converse of the pythagorean theorem. The regular version of the pythagorean theorem is the reverse (which says if we had a right triangle then a^2+b^2 = c^2 is true)
We have
a = 4
b = 9
c = 12
The order of a,b doesn't matter. So we could have a = 9 and b = 4. Usually 'a' is the smallest of the trio. All that matters is that c is the largest value.
Plug those values into the equation mentioned
a^2 + b^2 = c^2
4^2 + 9^2 = 12^2
16 + 81 = 144
97 = 144
The last equation is false, so the first equation must also be false when (a,b,c) = (4,9,12)
Answer: This is not a right triangle.
|
|
|
