document.write( "Question 101884: 5.A triangle has the following sides: 12 feet, 20 feet, and 16 feet. Is this a right triangle? Explain your answer. \n" ); document.write( "

Algebra.Com's Answer #74080 by doukungfoo(195) $\"\"$ $\"About$

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.
\n" ); document.write( "The pythagorean formula is:
\n" ); document.write( " $\"a%5E2%2Bb%5E2=c%5E2\"$
\n" ); document.write( "c is the hypotenuse
\n" ); document.write( "a is one side of the triangle
\n" ); document.write( "b is the remaining side of the triangle
\n" ); document.write( "Lets see what we get:
\n" ); document.write( " $\"a%5E2%2Bb%5E2=c%5E2\"$
\n" ); document.write( " $\"16%5E2%2B12%5E2=20%5E2\"$
\n" ); document.write( " $\"256%2B144=400\"$
\n" ); document.write( " $\"400=400\"$
\n" ); document.write( "The pythagorean formula only works with right triangles. So we can be sure that the given triangle is a right triangle.
\n" ); document.write( " \n" ); document.write( "

\n" );