When a square piece of paper is folded in half vertically, the resulting rectangle has a perimeter of 39cm. In square centimeters, find the area of the original square piece of paper.
Let x = side of square
2(.5x) + 2x = 39
3x = 39
x = 13
x^2 = ?
the area of the original square piece of paper are 169
Let's denote the side length of the original square piece of paper as x cm.
When the paper is folded in half vertically, the resulting rectangle has a perimeter of 39 cm. Since the length of the rectangle is equal to one side of the original square piece, it is x/2 cm. The width of the rectangle is also x/2 cm.
The perimeter of a rectangle is given by the formula P = 2(length + width). So we have:
39 cm = 2(x/2 + x/2)
Simplifying the equation, we get:
39 cm = x
Therefore, the side length of the square piece of paper is 39 cm.
The area of a square is given by the formula A = side^2. Plugging in the value we just found, we have:
A = (39 cm)^2
A = 1521 cm^2
Therefore, the area of the original square piece of paper is 1521 square centimeters.
To find the area of the original square piece of paper, we need to determine the length of one side of the square.
Let's assume that the length of one side of the square is "x" cm.
When the square is folded in half vertically, the resulting rectangle has a perimeter of 39 cm.
Since the rectangle's perimeter is the sum of all its sides, we can deduce that the sum of the two shorter sides of the rectangle is equal to the length of one side of the original square.
So, the sum of the two shorter sides of the rectangle is 2x cm.
Since the longer side of the rectangle is formed by folding the square in half, its length is "2x" cm.
The perimeter of the rectangle is given as 39 cm, so we can write the following equation:
2x + 2x + 39 = 39
Simplifying this equation:
4x + 39 = 39
4x = 0
Dividing both sides of the equation by 4, we find:
x = 0
This result indicates that something went wrong in the calculations. It is not possible for the length of one side of the square to be zero.
However, let's revisit the equation and reason about the problem:
2x + 2x + 39 = 39
If we look closely, we can see that the sum of 2x and 2x is equal to 4x. Therefore, the equation can be rewritten as:
4x + 39 = 39
Subtracting 39 from both sides:
4x = 0
Dividing both sides of the equation by 4:
x = 0
This implies that the length of one side of the original square is zero. However, this is not possible since a square must have positive dimensions.
Therefore, the given information does not provide a valid solution to find the area of the original square piece of paper.