A rectangle has a diagonal of 13 cm and one side of 5 cm. What is the area of the rectangle?
["Understanding Rectangles: Given a Diagonal of 13 cm and One Side of 5 cm, Find the Area", "When studying geometry, one of the most common problems involves finding unknown dimensions of a rectangle using its diagonal and one side length. Whether you’re solving a textbook exercise or tackling a real-world measurement, clarity is key. In this article, we’ll explore how to determine the area of a rectangle with a diagonal measuring 13 cm and one side measuring 5 cm.", "---", "### What You Need to Know: Rectangle Diagonals and Sides", "A rectangle’s diagonals are equal in length and divide the shape into two identical right-angled triangles. According to the Pythagorean theorem, the relationship between the sides (a), (b), and the diagonal (d) is:", "[\nd^2 = a^2 + b^2\n]", "In our case:", "- Diagonal (d = 13) cm\n- One side (a = 5) cm\n- The unknown side (b) needs to be found\n- Finally, the area (A = a \ imes b) will be calculated", "---", "### Step-by-Step Calculation", "1. Apply the Pythagorean theorem:", "[\n13^2 = 5^2 + b^2\n]", "[\n169 = 25 + b^2\n]", "2. Solve for (b^2):", "[\nb^2 = 169 - 25 = 144\n]", "3. Find (b):", "[\nb = \sqrt{144} = 12 \ ext{ cm}\n]", "---", "### Calculate the Area", "With both side lengths known — (a = 5) cm and (b = 12) cm — the area (A) is:", "[\nA = 5 \ imes 12 = 60 \ ext{ cm}^2\n]", "---", "### Conclusion", "Given a rectangle with a diagonal of 13 cm and one side of 5 cm, the area is 60 square centimeters. Understanding this foundational relationship empowers you to solve similar geometry problems confidently. Remember, the Pythagorean theorem is your guide when dealing with right triangles formed by a rectangle’s diagonal and sides.", "---", "Keywords: rectangle diagonal 13 cm, find rectangle area, diagonal and side length, right triangle in rectangle, geometry problem solution, Pythagorean theorem rectangle, 5 cm rectangle side area", "Meta Description: Learn how to find the area of a rectangle with a diagonal of 13 cm and one side measuring 5 cm. Step-by-step solution using the Pythagorean theorem.\nHeader Tag: How to Calculate the Area of a Rectangle Using Diagonal and One Side", "---", "By mastering these concepts, you gain not only the answer but also the tools to tackle more advanced geometry challenges with clarity and confidence."]
