Explain why the perimeter:Area ratio value can be used to understand cost effectiveness
perimeter defines the length and therefore cost of fencing.
area defines the size of the enclosure, for example how much grass for the cows to munch.
the minimum fence length for maximum grass is the perimeter to area ratio.
Example for rectangle:
What are the dimensions of a rectangular field that surrounds the maximum area with 100 meters of fence?
x+y = 50
A = x y
if it is square:
25 on a side
area = 625
if one side is longer, for example 10 by 40
area = 400
least fence cost for square, x/y = 1
perimeter/area = 4 x/x^2 = 4/x
to find the total area under sq.feet
The perimeter:Area ratio value is a mathematical concept that relates the perimeter of a shape to its area. It is calculated by dividing the perimeter of the shape by its area. This ratio can be used to understand the cost-effectiveness of a shape, particularly in construction or landscaping projects.
When designing a structure or planning a landscape, it is important to consider the cost of the materials required to build or maintain the area. The perimeter represents the length of the outer boundary of the shape, which usually requires more materials such as fencing or boundary markers. On the other hand, the area represents the actual space enclosed within the shape, which determines the amount of ground to be covered or filled.
By calculating the perimeter:Area ratio, we can compare different shapes and determine their cost-effectiveness. A shape with a low ratio indicates that it has a larger area in relation to its perimeter. This means that it maximizes the enclosed space while minimizing the length of the outer boundary, thus potentially reducing costs.
On the contrary, a shape with a high ratio has a larger perimeter relative to its area. This suggests that it requires more materials to enclose a given space, which may result in increased costs. In such cases, it might be worth considering alternative shapes or designs with lower ratios to improve cost-effectiveness.
Overall, the perimeter:Area ratio value helps in evaluating the efficiency of different shapes or structures by considering the relationship between perimeter and area. By analyzing this ratio, one can make informed decisions about design choices to achieve the desired cost effectiveness in construction or landscaping projects.