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*