a 2d regular box has a perimeter of 200cm determine the maximum possible area
To determine the maximum possible area of a 2D regular box with a given perimeter of 200cm, we need to understand the properties of a regular box.
A regular box is a rectangular shape with all sides being equal in length. Let's assume the length of one side (or base) is 'x' cm. Since a regular box has four equal sides, the perimeter can be calculated as 4 times the length of one side, which gives us:
Perimeter = 4x
Given that the perimeter is 200cm, we can set up the following equation:
4x = 200
Now, let's solve for 'x' to find the length of each side:
Divide both sides of the equation by 4:
x = 200 / 4
x = 50
So, each side of the regular box is 50 cm.
To find the maximum possible area, we can use the formula for the area of a rectangle, which is given by:
Area = length * width
In this case, since the box is regular, the length and width are equal, so we can simply square the length of one side to find the maximum possible area:
Area = x^2 = 50^2 = 2500 cm^2
Therefore, the maximum possible area of the 2D regular box is 2500 square centimeters.