If a square of side length x is cut in half, what is the perimeter of one of the resultant halves?
x/2 + x + x/2 + x = 3x
To find the perimeter of one of the resultant halves, let's first calculate the side length of the half square.
When a square with side length x is cut in half, each resultant half still has the same height (or side length) as the original square but half the width.
So, the side length of the half square is x/2.
The perimeter of a square is calculated by adding up the lengths of all its sides. Since the half square has four equal sides, we multiply the half square's side length by 4 to get the perimeter.
Therefore, the perimeter of one of the resultant halves of a square with side length x is 4 * (x/2) = 2x.
To find the perimeter of one of the resultant halves, we need to understand how the cut is made. If a square of side length x is cut in half, it can be done either vertically or horizontally. Let's consider both cases:
1. Cut is made vertically:
In this case, the square is divided into two rectangles of dimensions x/2 and x. The perimeter of one of the resultant halves is given by:
Perimeter = 2 * (x/2 + x) = 2 * (x + x/2) = 2 * (3x/2) = 3x.
2. Cut is made horizontally:
In this case, the square is divided into two rectangles of dimensions x and x/2. The perimeter of one of the resultant halves is given by:
Perimeter = 2 * (x + x/2) = 2 * (3x/2) = 3x.
Thus, regardless of whether the square is cut vertically or horizontally, the perimeter of one of the resultant halves is equal to 3x.