At an outdoor festival, 2-m sections of fencing are used to enclose an area for food sales. there are 100 sections of fencing available.
a) how many metres of fencing are available altogether?
my answer for question a:
100* 2 = 200m
b) determine the maximum rectangular area that could be enclosed. How does the fact that the fencing is in sections affect your answer?
can someone help me on question b and correct question A
for a given perimeter, the square has maximum area
so, if there are 100 sections of fence, a square with 25 sections on each side will have maximum area.
(25*2)^2 = 50^2 = 2500 m^2
correct on A.
dimensions will have to be in 2 meter increments. 100 of them. Max area will be 10 sections by 10 sections (a square), or 20 m x 20 m.
can you help me on question b, i really don't know how to do it
For question A, you are correct in calculating the total length of fencing. To find the total length of fencing available, you multiply the number of sections (100) by the length of each section (2m). So, the correct calculation is:
Total length of fencing = 100 sections * 2m/section = 200m
Now, let's move on to question B. To determine the maximum rectangular area that can be enclosed, we need to consider how the fencing is arranged. Since the fencing is in sections, we can't freely adjust its length. Each section is fixed at a length of 2m.
To maximize the rectangular area, we should aim for a square-shaped enclosure. This is because a square has the largest area for a given perimeter.
Let's assume we use the fencing to create a square enclosure. Since each side of a square is equal, we can divide the total length of fencing (200m) by the perimeter of a square to find the length of each side.
Perimeter of a square = 4 * side length (since all sides are equal)
So, the side length of the square can be calculated as:
Side length = Total length of fencing / 4 = 200m / 4 = 50m
Now, we can determine the maximum rectangular area by multiplying the side length by itself:
Maximum rectangular area = Side length * Side length = 50m * 50m = 2500 square meters
Therefore, the maximum rectangular area that could be enclosed using the available fencing is 2500 square meters.