a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?
To find the maximum area that can be enclosed with 1000m fencing, we need to determine the dimensions of the rectangular storage area that would use up all the fencing.
Let's assume the length of the rectangular storage area is L, and the width is W.
We know that a rectangular area has two equal length sides and two equal width sides.
To maximize the area, we want to maximize the length and minimize the width. Therefore, we can assume that the width will be as small as possible, which means it will be zero.
Since we have three sides that need fencing (two lengths and one width), we can calculate the total length of fencing needed as follows:
2L + W = 1000m
Since we assumed the width would be zero, the equation becomes:
2L + 0 = 1000m
2L = 1000m
L = 500m
Therefore, the length of the rectangular storage area would be 500m, and the width would be zero.
Now, to calculate the maximum area that can be enclosed, we use the formula for the area of a rectangle:
Area = Length x Width
Area = 500m x 0m
Area = 0m²
Therefore, the maximum area that can be enclosed with 1000m of fencing is 0 square meters.