Do the three sides make a right triangle?

The lengths of the three sides of a triangle are 10, 14, and 18 inches.  Determine whether this triangle is a right triangle.

In a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.
Also, the hypotenuse is the longest side of a right triangle.

a² + b² = c²   {Pythagorean Theorem says sum of squares of legs equals square of hypotenuse}
10² + 14² = 18²   {substituted given lengths into Pythagorean Theorem}
100 + 196 = 324   {evaluated exponents}
296 ≠ 324   {added on left side}

The triangle is not a right triangle.

- Algebra House