Understanding Park Design Constraints
When it comes to designing parks, there are certain constraints that must be considered. One common constraint is the perimeter of the park, which dictates the length of the boundary surrounding the park. In this case, we are looking at a rectangular park with a perimeter of 80m.
Calculating Area of a Rectangle
The area of a rectangle is calculated by multiplying its length and width. In this scenario, we are given that the area of the park is 400 square meters. So, we can use this information to calculate the possible dimensions of the park.
Is it Possible?
Let’s break it down. If we let the length of the park be ‘l’ and the width be ‘w’, we know that the perimeter is given by the formula 2(l+w) = 80. Simplifying, we get l+w = 40.
Since we also know that the area of the park is 400 square meters, we have the equation l * w = 400. Now, we have two equations with two variables. By solving them simultaneously, we can determine if it is possible to design a rectangular park with the given perimeter and area.
Solving for Dimensions
By substituting l = 40 – w from the first equation into the second equation, we get (40 – w) * w = 400. Simplifying, we get w^2 – 40w + 400 = 0. Solving this quadratic equation, we get two possible widths: w=20 or w=20.
Substituting these values back into the equation l+w = 40, we find the corresponding lengths: l=20 or l=20. Therefore, it is indeed possible to design a rectangular park with a perimeter of 80m and an area of 400 square meters. The dimensions would be 20m x 20m.
Conclusion
Designing a park with specific constraints like perimeter and area requires careful calculation and consideration of mathematical formulas. In this case, we have shown that it is possible to create a rectangular park with the given perimeter and area. By understanding the relationships between length, width, perimeter, and area, park designers can create beautiful and functional green spaces that meet the desired specifications.
