**Problem Statement:**The figure below is a square. Find the length of side \( x \) in simplest radical form with a rational denominator.![Diagram of a square with a diagonal line segment](insert_image_url_here)In the diagram, one of the sides of the square is labeled as \( 9 \) and the diagonal is labeled as \( x \).**Solution:**To solve this problem, we need to recall the property of a square's diagonal. 1. Let's denote the side of the square as \( s \). For a square, all sides are equal, so each side length is \( s = 9 \).2. The diagonal \( x \) of the square is related to the side length by the formula:\[x = s \sqrt{2}\]3. Substituting \( s = 9 \):\[x = 9 \sqrt{2}\]Thus, the length of the diagonal \( x \) in simplest radical form is \( 9\sqrt{2} \).**Answer:**The length of side \( x \) in simplest radical form with a rational denominator is \( 9\sqrt{2} \).**Diagram Explanation:**The diagram shows a square with one side labeled as 9 units. A diagonal line segment divides the square into two right triangles, creating sides of \( 9 \) units and a hypothenuse labeled as \( x \). In this setup, we used the Pythagorean theorem in combination with properties of squares to determine the length of the diagonal.

Name: **Problem Statement:**The figure below is a square. Find the length o
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: **Problem Statement:**The figure below is a square. Find the length of side \( x \) in simplest radical form with a rational denominator.![Diagram of a square with a diagonal line segment](insert_image_url_here)In the diagram, one of the sides of th