A square and a rectangle each have a perimeter of 100 feet. Explain how this is possible.
Side of Square is 25 feet.
One side of rectangle is 30 feet and other is 20 feet.
There is an infinite number of rectangles which have the same perimeter as the square with perimeter of 100
As long as the length and width of the rectangle add up to 50
e.g.
10 and 40
1 and 49
3.567 and 46.433
√46 and (50-√46)
etc.
To understand how a square and a rectangle can have the same perimeter, let's start by defining perimeter. The perimeter of a shape is the total distance around its outer boundary.
Let's assume the square has equal sides, so all its sides are of equal length. Let's call this length 'x'. Since a square has four equal sides, its perimeter is given by the formula:
Perimeter of square = 4 * x
Since the perimeter of the square is 100 feet, we can set up the equation:
4 * x = 100
Now, let's consider the rectangle. A rectangle has two pairs of opposite sides that are equal in length. Let's call the length of one pair of equal sides 'y', and the other pair 'z'. The perimeter of a rectangle is given by the formula:
Perimeter of rectangle = 2 * (y + z)
For the rectangle to have the same perimeter as the square (100 feet), we can set up the equation:
2 * (y + z) = 100
Now, to explore how a square and a rectangle can have the same perimeter, we need to find possible values of 'x', 'y', and 'z' that satisfy both equations simultaneously.
By solving the first equation, 4 * x = 100, we find that x = 25.
Substituting this value of x into the second equation, 2 * (y + z) = 100, we get:
2 * (y + z) = 100
2 * (y + z) = 2 * (25)
y + z = 25
So, the values of 'y' and 'z' can be any numbers that add up to 25.
For instance, if we choose y = 10 and z = 15, we have:
y + z = 10 + 15 = 25
This satisfies both the equations and gives us a square and a rectangle with the same perimeter of 100 feet.
In summary, a square and a rectangle can have the same perimeter if the square has sides of length 25 feet, and the rectangle has one pair of opposite sides with a length of 10 feet and the other pair with a length of 15 feet.