Calculate The Side Length Of Ob In A 2024

How to Calculate the Side Length of OB in a Rectangle Using Geometry and the Pythagorean Theorem

Learn how to find the side length of OB in a rectangle through geometry and the Pythagorean theorem. Discover the principles of parallel sides and right triangles in this step-by-step tutorial.

In this video, we learn how to find the side length of OB in a rectangle using geometry and the Pythagorean theorem.
We utilize the fact that opposite sides of a rectangle are parallel and equal to each other, and the corners are right triangles.
By applying the Pythagorean theorem and creating parallel lines, we can effectively solve this geometry problem.

In this instructional video, we delve into the world of geometry to solve the problem of finding the side length of OB in a rectangle. We use key principles of geometry, including parallel lines, right triangles, and the Pythagorean theorem, to arrive at the solution.

Point O is within the rectangle ABCD, with OA measuring one unit, OD three units, and OC four units. Since ABCD is a rectangle, we draw line segments EF and GH through point O, parallel to lines AB and AD, respectively.
By utilizing the concept of same-side interior angles, we determine that angle A plus angle AEF equals 180 degrees. As angle A is a right angle (90 degrees), angle AEF is also 90 degrees, making it a right angle.
Applying the Pythagorean theorem, we introduce variables a, b, c, and d to represent the side lengths of AE, ED, HG, and GB, respectively. We then establish four equations to relate these variables to the known side lengths of OA, OD, OC, and OB.
We focus on finding a squared and d squared. By subtracting equation two from equation one and adding equation three, we eliminate c squared and obtain a squared minus b squared. Adding the term b squared and d squared results in a squared plus d squared.
The equation a squared plus d squared equals OB squared. Through this, we discover that OB equals 2 square root 2. This method demonstrates the application of geometric principles and the Pythagorean theorem in solving complex problems.

In summary, this video teaches us to utilize the properties of rectangles, including parallel sides and right angles, to simplify complex geometry problems. By creating parallel lines and forming right triangles, we can effectively use the Pythagorean theorem to find unknown side lengths. Geometry enthusiasts and learners will benefit from understanding these fundamental concepts in solving geometric puzzles. Don't forget to subscribe for more educational content. Goodbye!

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