Geometry
Pythagorean Theorem

For the following right triangle, find the side length 20, 16 , x Round your answer to the nearest hundredth.

Step 1 ：Given a right triangle with side lengths 20, 16, and x, where x is the unknown side length.

Step 2 ：According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This can be written as: \(a² + b² = c²\).

Step 3 ：In this case, we know the lengths of two sides (20 and 16) and we need to find the length of the third side (x). Since the lengths of the known sides are greater than x, we can assume that these sides form the hypotenuse.

Step 4 ：Therefore, we can rearrange the Pythagorean theorem to solve for x: \(x = \sqrt{c² - b²}\).

Step 5 ：Substituting the given values into the equation, we get \(x = \sqrt{20² - 16²}\).

Step 6 ：Solving the equation, we find that \(x = 12.0\).

Step 7 ：Final Answer: The length of the side x is \(\boxed{12.0}\).