The problem involves a square placed diagonally inside a rectangle, and we are tasked with finding the value of $X$, which is the horizontal length of the rectangle. Here's how we can solve this step-by-step:

Step 1: Understanding the Figure

• The square is tilted inside the rectangle.
• The length of one side of the square is $12$ units.
• The height of the rectangle (vertical side) is $9$ units.
• We are looking for the length of the rectangle, labeled as $X$.

Step 2: Geometry Involved

The diagonal of the square creates a right triangle inside the rectangle. Using the properties of the square and right triangles, we can set up equations to solve for $X$.

• The side length of the square is $12$.
• The