A wire of length 24 meter is to be folded in the form of a rectangle. If each side of a rectangle has to be an integer (measured in meters), what is the maximum number of rectangles that can be formed by folding the wire?
the width+length must be 12. So, start listing pairs of integers which add to 12:
1,11
2,10
...
6,6
To find the maximum number of rectangles that can be formed by folding a wire of length 24 meters, we need to consider the possible dimensions of the rectangle.
Let's denote the length of one side of the rectangle as 'l' and the width as 'w'. Since the wire length is 24 meters, we have 2l + 2w = 24.
One important thing to note is that the rectangle should have integer side lengths. This means that both 'l' and 'w' must be positive integers.
To find the maximum number of rectangles, we need to find all possible pairs of (l, w) that satisfy the equation 2l + 2w = 24 and are positive integers.
To make the calculations easier, let's divide the equation by 2: l + w = 12.
Now, we can iterate through the possible values for 'l' from 1 to 11 (since 'w' will be 12 - 'l'), and check if the resulting values for 'l' and 'w' are positive integers.
By doing this, we find the following pairs: (1, 11), (2, 10), (3, 9), (4, 8), (5, 7), and (6, 6).
Therefore, there are six possible rectangles that can be formed by folding the wire: one with sides 1 meter and 11 meters, one with sides 2 meters and 10 meters, and so on.
Thus, the maximum number of rectangles that can be formed by folding the wire is 6.