The Total Cost Of Painting A Square Wall At ₹15 Per M² Is ₹1815. Find The Length Of One Side Of The Wall.​

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Introduction

In this article, we will delve into the world of mathematics and explore the concept of finding the length of one side of a square wall given its total cost of painting. We will use the given information that the total cost of painting the wall is ₹1815 at a rate of ₹15 per m² to determine the length of one side of the wall.

Understanding the Problem

The problem states that the total cost of painting a square wall is ₹1815 at a rate of ₹15 per m². To find the length of one side of the wall, we need to use the formula for the area of a square, which is given by:

Area = side²

We are also given the total cost of painting the wall, which is ₹1815, and the rate at which the wall is painted, which is ₹15 per m².

Breaking Down the Problem

To solve this problem, we need to break it down into smaller steps. First, we need to find the total area of the wall in square meters. We can do this by dividing the total cost of painting the wall by the rate at which the wall is painted.

Total Area = Total Cost / Rate = ₹1815 / ₹15 per m² = 121 m²

Now that we have the total area of the wall, we can use the formula for the area of a square to find the length of one side of the wall.

Finding the Length of One Side of the Wall

We know that the area of a square is given by:

Area = side²

We also know that the total area of the wall is 121 m². Therefore, we can set up the equation:

121 = side²

To find the length of one side of the wall, we need to take the square root of both sides of the equation.

side = √121 = 11 m

Therefore, the length of one side of the wall is 11 m.

Conclusion

In this article, we explored the concept of finding the length of one side of a square wall given its total cost of painting. We used the formula for the area of a square and the given information to determine the length of one side of the wall. We found that the length of one side of the wall is 11 m.

Mathematical Formulas Used

  • Area of a square: Area = side²
  • Total Area = Total Cost / Rate
  • side = √Area

Real-World Applications

This problem has real-world applications in various fields such as architecture, engineering, and construction. For example, in architecture, the length of one side of a square wall can be used to determine the total area of the wall, which is necessary for designing and building the wall. In engineering, the length of one side of a square wall can be used to determine the total volume of the wall, which is necessary for designing and building the wall.

Tips and Tricks

  • When solving problems involving the area of a square, make sure to use the correct formula: Area = side².
  • When solving problems involving the total area of a wall, make sure to use the correct formula: Total Area = Total Cost / Rate.
  • When solving problems involving the length of one side of a square wall, make sure to take the square root of both sides of the equation.

Frequently Asked Questions

  • What is the total cost of painting a square wall?
    • The total cost of painting a square wall is ₹1815.
  • What is the rate at which the wall is painted?
    • The rate at which the wall is painted is ₹15 per m².
  • What is the length of one side of the wall?
    • The length of one side of the wall is 11 m.
      The Total Cost of Painting a Square Wall: A Q&A Guide ===========================================================

Introduction

In our previous article, we explored the concept of finding the length of one side of a square wall given its total cost of painting. We used the formula for the area of a square and the given information to determine the length of one side of the wall. In this article, we will provide a Q&A guide to help you understand the concept better.

Q&A Guide

Q: What is the total cost of painting a square wall?

A: The total cost of painting a square wall is ₹1815.

Q: What is the rate at which the wall is painted?

A: The rate at which the wall is painted is ₹15 per m².

Q: What is the length of one side of the wall?

A: The length of one side of the wall is 11 m.

Q: How do I find the total area of the wall?

A: To find the total area of the wall, you need to divide the total cost of painting the wall by the rate at which the wall is painted. The formula is:

Total Area = Total Cost / Rate

Q: What is the formula for the area of a square?

A: The formula for the area of a square is:

Area = side²

Q: How do I find the length of one side of the wall?

A: To find the length of one side of the wall, you need to take the square root of both sides of the equation. The formula is:

side = √Area

Q: What are the real-world applications of this concept?

A: This concept has real-world applications in various fields such as architecture, engineering, and construction. For example, in architecture, the length of one side of a square wall can be used to determine the total area of the wall, which is necessary for designing and building the wall. In engineering, the length of one side of a square wall can be used to determine the total volume of the wall, which is necessary for designing and building the wall.

Q: What are some tips and tricks for solving problems involving the area of a square?

A: Here are some tips and tricks for solving problems involving the area of a square:

  • When solving problems involving the area of a square, make sure to use the correct formula: Area = side².
  • When solving problems involving the total area of a wall, make sure to use the correct formula: Total Area = Total Cost / Rate.
  • When solving problems involving the length of one side of a square wall, make sure to take the square root of both sides of the equation.

Q: What are some common mistakes to avoid when solving problems involving the area of a square?

A: Here are some common mistakes to avoid when solving problems involving the area of a square:

  • Not using the correct formula for the area of a square.
  • Not using the correct formula for the total area of a wall.
  • Not taking the square root of both sides of the equation when solving problems involving the length of one side of a square wall.

Conclusion

In this article, we provided a Q&A guide to help you understand the concept of finding the length of one side of a square wall given its total cost of painting. We hope that this guide has been helpful in clarifying any doubts you may have had.

Mathematical Formulas Used

  • Area of a square: Area = side²
  • Total Area = Total Cost / Rate
  • side = √Area

Real-World Applications

This concept has real-world applications in various fields such as architecture, engineering, and construction. For example, in architecture, the length of one side of a square wall can be used to determine the total area of the wall, which is necessary for designing and building the wall. In engineering, the length of one side of a square wall can be used to determine the total volume of the wall, which is necessary for designing and building the wall.

Tips and Tricks

  • When solving problems involving the area of a square, make sure to use the correct formula: Area = side².
  • When solving problems involving the total area of a wall, make sure to use the correct formula: Total Area = Total Cost / Rate.
  • When solving problems involving the length of one side of a square wall, make sure to take the square root of both sides of the equation.

Frequently Asked Questions

  • What is the total cost of painting a square wall?
    • The total cost of painting a square wall is ₹1815.
  • What is the rate at which the wall is painted?
    • The rate at which the wall is painted is ₹15 per m².
  • What is the length of one side of the wall?
    • The length of one side of the wall is 11 m.