sketch a number of pens that can be constructed using 24 m of fencing
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using a table of values, record the lenght and widths of each pen cosntructed using 24 m of fencing
To determine the number of pens that can be constructed using 24 meters of fencing, we need to consider the perimeter of each pen.
Let's assume the shape of the pen is rectangular. In this case, the total length of the fencing will be equal to the sum of the lengths of all sides of the pen.
Let's say the length of the pen is L and the width of the pen is W. The perimeter can be calculated as:
Perimeter = 2L + 2W
Since we have 24 meters of fencing available, we can set up the equation:
2L + 2W = 24
Now, we need to determine the values of L and W that satisfy this equation.
One approach is to list out all possible combinations of L and W that would yield a total perimeter of 24 meters.
Let's begin by starting with L = 1 meter and incrementing the value of L by 1 each time. We can then find the corresponding value of W using the equation we derived above.
L = 1 -> 2(1) + 2W = 24 -> 2W = 22 -> W = 11
Hence, for L = 1, W = 11 yields a total perimeter of 24 meters.
By repeating this process and incrementing L by 1, we can find other valid combinations of L and W:
L = 2 -> 2(2) + 2W = 24 -> 2W = 20 -> W = 10
L = 3 -> 2(3) + 2W = 24 -> 2W = 18 -> W = 9
Continuing this pattern, we can find the following valid combinations:
L = 4, W = 8
L = 5, W = 7
L = 6, W = 6
Note that for L = 6 and W = 6, we have a square-shaped pen.
So, based on the calculations, we can construct 5 pens using a total of 24 meters of fencing - one each for the combinations (1, 11), (2, 10), (3, 9), (4, 8), and (5, 7).
Each of these pens will have a different shape and size, but the total perimeter will be 24 meters in all cases.