Pythagorean Theorem Examples

Find the missing side of this triangle.

The length of the hypotenuse is missing, and we are given the lengths of the legs: 5 and 12.

Plugging these numbers into the Pythagorean Theorem, we get

5² + 12² = x²

25 + 144 = x²

169 = x²

To solve for x when it's being squared, we have to find the square root of both sides.

So x = 13.

Find the length of the missing side of this right triangle.

The length of a leg is missing, and we are given the lengths of the other leg and the hypotenuse.

The length of a leg is missing, and we are given the lengths of the other leg and the hypotenuse.

The other leg is 15 cm and the hypotenuse is 17 cm. Plugging those numbers into the Pythagorean Theorem, we get:

x² + 15² = 17²

When we simplify the exponents, we get

x² + 225 = 289

x² = 289 – 225

x^{2 =} 64

So x = 8.

Is a triangle with side lengths of 4 cm, 7 cm, and 8 cm a right triangle?

If it is a right triangle, then the sum of the squares of the two smaller sides will equal the square of the largest side.

If it is a right triangle, 4² + 7² = 8², but does it?

Does 16 + 49 equal 64?

65 ≠ 64

Lo and behold, 65 does not equal 64 so 4 cm, 7 cm, and 8 cm could not be the lengths of a right triangle.