**Educational Website Transcription**---### Geometry: Solving for the Unknown in a Rectangle**Problem Statement:**For the rectangle shown, which equation can be used to find the value of \(x\)?**Diagram Explanation:**In the provided rectangle, one side is labeled with a length of 5 units, another side is labeled with a length of \(x\) units, and the diagonal of the rectangle is labeled with a length of 12 units. A right angle is indicated between the two sides labeled 5 and \(x\).**Options:**A) \(5 + 12 = x^2\)B) \(5^2 + 12^2 = x^2\)C) \(5^2 + x^2 = 12^2\)D) \((x + 5)^2 = 12^2\)**Analysis:**To find which equation can be used to determine \(x\), we should use the Pythagorean theorem. In a right triangle, the theorem states that the sum of the squares of the two legs is equal to the square of the hypotenuse. Thus, for this rectangle:\(5^2 + x^2 = 12^2\)So, the correct option is:C) \(5^2 + x^2 = 12^2\)**Educational Insight:**Understanding and applying the Pythagorean theorem is crucial when working with right triangles. By successfully identifying and utilizing the theorem, you can solve for unknown side lengths in various geometric figures.---*Use the above information to guide your practice in solving problems involving right triangles and the Pythagorean theorem.*

Name: **Educational Website Transcription**---### Geometry: Solving for the
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Educational Website Transcription**---### Geometry: Solving for the Unknown in a Rectangle**Problem Statement:**For the rectangle shown, which equation can be used to find the value of \(x\)?**Diagram Explanation:**In the provided rectangle, one s