The Area Of A Square Hall Is 625 M² If The Length Is 25 M What Is The Breath
**The Area of a Square Hall: A Historical Perspective** =====================================================
Introduction
In the realm of geometry, the area of a square is a fundamental concept that has been studied and applied for centuries. A square is a quadrilateral with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one side by itself. In this article, we will delve into the concept of the area of a square and explore a historical problem involving a square hall with an area of 625 m².
The Problem
A square hall has an area of 625 m². If the length of one side of the hall is 25 m, what is the breadth of the hall?
History of Geometry
Geometry has a rich and fascinating history that spans thousands of years. The ancient civilizations of Egypt, Greece, and Babylon made significant contributions to the development of geometry. The Pythagorean theorem, which relates the lengths of the sides of a right triangle, was known to the ancient Babylonians as early as 1900 BCE.
The Pythagorean Theorem
The Pythagorean theorem is a fundamental concept in geometry that states:
a² + b² = c²
where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse (the side opposite the right angle).
Solving the Problem
To solve the problem, we need to use the formula for the area of a square:
Area = side²
We are given that the area of the square hall is 625 m², and the length of one side is 25 m. We can set up an equation using the formula for the area of a square:
25² = 625
To find the breadth of the hall, we need to find the length of the other side. Since the hall is a square, all sides are equal. Therefore, the breadth of the hall is also 25 m.
Q&A
Q: What is the area of a square? A: The area of a square is calculated by multiplying the length of one side by itself.
Q: How do you find the breadth of a square hall if you know the area and the length of one side? A: To find the breadth of a square hall, you need to use the formula for the area of a square and set up an equation. Since all sides of a square are equal, the breadth of the hall is also equal to the length of one side.
Q: What is the Pythagorean theorem? A: The Pythagorean theorem is a fundamental concept in geometry that relates the lengths of the sides of a right triangle.
Q: How do you use the Pythagorean theorem to solve problems involving right triangles? A: To use the Pythagorean theorem, you need to identify the lengths of the legs of the right triangle and the length of the hypotenuse. Then, you can plug these values into the equation a² + b² = c² to solve for the unknown side.
Conclusion
In conclusion, the area of a square is a fundamental concept in geometry that has been studied and applied for centuries. The problem of finding the breadth of a square hall with an area of 625 m² and a length of one side of 25 m is a classic example of how geometry can be used to solve real-world problems. By using the formula for the area of a square and the Pythagorean theorem, we can find the breadth of the hall and gain a deeper understanding of the principles of geometry.
Additional Resources
Frequently Asked Questions
- Q: What is the area of a square with a side length of 10 m? A: The area of a square with a side length of 10 m is 100 m².
- Q: How do you find the length of the hypotenuse of a right triangle? A: To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem: a² + b² = c².
- Q: What is the breadth of a square hall with an area of 400 m² and a length of one side of 20 m? A: The breadth of a square hall with an area of 400 m² and a length of one side of 20 m is 20 m.