An orchard planted on a square plot of land has 3,136 apple trees. If each tree requires an area of 4 square meters to grow, find the length of each side of the plot of land.
An orchard planted on a square plot of land has 3,136 apple trees. If each tree requires an area of 4 square meters to grow, find the length of each side of the plot of land.
Length = √(3,136*4)
To find the length of each side of the plot of land, we can use the formula for the area of a square.
Let's assume the length of each side of the square plot is 'x' meters.
The total number of apple trees is equal to the total area of the square plot divided by the area required for each tree.
The area of the square plot is given by:
Area = x^2
Since each tree requires an area of 4 square meters to grow, we can set up the equation:
Total number of apple trees = Area / Area required for each tree
3,136 = (x^2) / 4
To solve for x, we'll multiply both sides of the equation by 4:
4 * 3,136 = x^2
12,544 = x^2
Taking the square root of both sides gives:
x = √12,544
x ≈ 112
Therefore, the length of each side of the plot of land is approximately 112 meters.
To find the length of each side of the plot of land, we need to determine the total area occupied by the apple trees and then calculate the square root of that area.
First, let's calculate the total area occupied by the apple trees. We know that each tree requires an area of 4 square meters to grow, and there are 3,136 trees. Therefore, the total area required by the trees is:
Total Area = Number of Trees × Area per Tree
Total Area = 3,136 trees × 4 square meters per tree
Total Area = 12,544 square meters
Now, the length of each side of the square plot can be found by calculating the square root of the total area:
Length of Each Side = √Total Area
Length of Each Side = √12,544
Length of Each Side ≈ 112 meters
Therefore, the length of each side of the plot of land is approximately 112 meters.