Question:
In the chessboard if the rectangle form is 1296, find the total number of squares formed.
In the chessboard if the rectangle form is 1296, find the total number of squares formed.
Updated On: May 30, 2024
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Solution and Explanation
To find the total number of squares formed on a chessboard, including all sizes from 1x1 up to the largest square, you can use the following formula:
Total number of squares = \(\frac{(n^4+n^3+n^2)}{6}\)
In this case, since the rectangle has an area of 1296, we can find the length of one side by taking the square root of 1296:
Side length = √1296 = 36
Now we can substitute the value of n into the formula:
Total number of squares = \(\frac{(36^4+36^3+36^2)}{6}\)
Calculating this expression:
Total number of squares = \(\frac{(1296+11664+1296)}{6}\) = \(\frac{14256}{6}\) = 2376
Therefore, on a chessboard where the rectangle formed has an area of 1296, the total number of squares formed is 2376.
Total number of squares = \(\frac{(n^4+n^3+n^2)}{6}\)
In this case, since the rectangle has an area of 1296, we can find the length of one side by taking the square root of 1296:
Side length = √1296 = 36
Now we can substitute the value of n into the formula:
Total number of squares = \(\frac{(36^4+36^3+36^2)}{6}\)
Calculating this expression:
Total number of squares = \(\frac{(1296+11664+1296)}{6}\) = \(\frac{14256}{6}\) = 2376
Therefore, on a chessboard where the rectangle formed has an area of 1296, the total number of squares formed is 2376.
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Concepts Used:
Coordinate Geometry
Coordinate geometry, also known as analytical geometry or Cartesian geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a way to represent geometric figures and solve problems using algebraic equations and coordinate systems.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.