HOW MANY RECTANGLES CAN YOU DRAW WITH A PERIMETER OF 32 M, WHEN EACH SIDE IS A WHOLE NUMBER?
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To determine the number of rectangles that can be drawn with a perimeter of 32 m, we need to consider the possible dimensions of the rectangle. Since each side of the rectangle must be a whole number, we can start by listing out the potential lengths and widths of the rectangle.
1. Start by considering the side lengths from 1 m to 16 m, as the maximum length or width of the rectangle cannot be greater than half of the perimeter (32 m / 2 = 16 m).
2. For each length, find the corresponding width that would result in a perimeter of 32 m. To calculate the width, subtract the length from the total perimeter and divide the result by 2.
For example, if the length is 1 m, the width would be (32 m - 1 m) / 2 = 15.5 m. However, since the width must be a whole number, we can discard fractional values. Hence, for a length of 1 m, there is no corresponding whole number width.
3. Repeat step 2 for each potential length.
Length = 2 m: Width = (32 m - 2 m) / 2 = 15 m
Length = 3 m: Width = (32 m - 3 m) / 2 = 14.5 m (discard fractional values)
Length = 4 m: Width = (32 m - 4 m) / 2 = 14 m
Length = 5 m: Width = (32 m - 5 m) / 2 = 13.5 m (discard fractional values)
and so on...
4. Continue this process until you reach a length of 16 m.
Length = 16 m: Width = (32 m - 16 m) / 2 = 8 m
5. Count the number of valid combinations of length and width (whole numbers only) that result in a perimeter of 32 m.
For this specific example, the valid combinations are: (2 m, 15 m), (4 m, 14 m), (6 m, 13 m), (8 m, 12 m).
So, in this case, there are 4 rectangles that can be drawn with a perimeter of 32 m, where each side is a whole number. Note that the number of rectangles may vary depending on the specific values of the length and width for different perimeters.