SOLUTION: 5.A triangle has the following sides: 12 feet, 20 feet, and 16 feet. Is this a right triangle? Explain your answer.

Question 101884: 5.A triangle has the following sides: 12 feet, 20 feet, and 16 feet. Is this a right triangle? Explain your answer.
Found 2 solutions by Kalmetam, doukungfoo:
Answer by Kalmetam(43) (Show Source): You can put this solution on YOUR website!
well we have to go by
A^2+B^2=C^2
lets say the right triange is right side up...
that Diagonal is ALWAYS the longest.
so that MUST be twenty..

so lets say:
12=a 16=b 20=c
Now lets solve
a^2+b^2=c^2
144+b^2=c^2
144+256=c^2
144+256=400
c^2=400
The sqare root of 400 is 20..
This IS a Right Triangle
Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
The hypotenuse is always the longest side of a right triangle. So knowing this we can plug the length of these sides into the pythagorean formula and prove if it is a right triangle or not.
The pythagorean formula is:

c is the hypotenuse
a is one side of the triangle
b is the remaining side of the triangle
Lets see what we get:

The pythagorean formula only works with right triangles. So we can be sure that the given triangle is a right triangle.

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