StudentShare solutions

# The Fencing Problem - Essay Example

## Extract of sampleThe Fencing Problem

Let us consider the square of sides 'a.'
The Perimeter of square = Summation of all sides
= a + a + a + a
= 4 * a
The Perimeter is given as 1000m
1000 = 4 * a
a = 250m = each side of the square
Area of square:
A = a2
A = 2502
A = 62500m2
Hence if the shape the of the plot is square then the area that can be covered with the
fencing of 1000m is 62500m2
Rectangle:
Let the two sides of the rectangle be 'a' and 'b'
Case I: Let side b = 2 * a i.e. the sides are in the ratio of 2:1
The Perimeter of rectangle = sum of all sides
= 2 * (a + b)
Here b = 2a
P = 2 * (a + 2a)
1000 = 2 * (3 * a)
a = 166.6m and
b = 2 * 166.6 = 333.2m
Area of rectangle
A = a * b
A = 166.6 * 333.2
A = 55511m2
Hence if the shape the of the plot is rectangular with sides in the ratio of 2:1 then the area that can be covered with the fencing of 1000m is 55511m2.
Case II : Let the sides be in the ratio of 3:2 i.e. b = 1.5 * a
P = 2 * (a + b)
1000 = 2 * ( a + 1.5 * a)
1000 = 5 * a
a = 200m
b = 1.5 * a = 300m
Area of rectangle
A = a * b
A = 200 * 300
A = 60000m2
Hence if the shape the of the plot is rectangular with sides in the ratio of 3:2 then the area that can be covered with the fencing of 1000m is 60000m2.
Equilateral Triangle:
The equilateral triangle has three sides of the equal lengths.
Here the three sides of triangle (a) will have length as:
Total length of fencing/ 3
a = 1000/3
a = 333.3m
The area of equilateral triangle is given by:
A = * Base * Height
A = * a * H
The height of equilateral triangle is given by:
sin60 = H/ side of triangle (a)
H = sin60 * 333.3
(Angle 60o is the internal angle of the equilateral triangle)
H = 289m
A = * 333.3 * 289
A = 48098m2
Hence if the shape the of the...
In this essay we shall first study the circle considering the perimeter as the circumference and from that finding the radius of the circle which than gives the area of the circle which can be covered with 1000m of the fence.
Then we shall consider the square shape, for which first we shall find the sides of the square and then the area of the square. Thereafter we shall consider rectangle; in this we shall consider the sides of ratios 2:1 and 3:2, with the procedure same as that of the square.
Then further we shall consider the triangle; first equilateral triangle is considered. For this the sides and the height of the triangle are found out and from that we get the area of the triangle. Then we have considered other two triangles; isosceles triangle and right angled triangle with the similar calculations.
Thereafter various polygons are considered. Beginning with the pentagon its sides and the height are found and from that the area of the pentagon is found out. Similar approach is followed for the hexagon and the octagon.
In the essay detailed calculations are shown for the various areas. The shape, which gives the maximum area, is also found and then the recommendations accordingly have been made. The calculations carried out are simple mathematical calculations.
Pentagon is a type of the polygon with five sides. The sum of total angles inside the polygon is 3600. ...Show more

## Summary

Aim: A farmer has exactly 1000 meters of fencing and wants to fence a plot of a level land. Our aim is to find out the shape in which maximum area of the plot will be covered. For this we shall calculate areas of the plots of various shapes.
Introduction: The farmer has a fence of 1000 meters and wants to fence of the plot…
Author : imcclure
Save Your Time for More Important Things
Let us write or edit the essay on your topic
"The Fencing Problem"
with a personal 20% discount.
Grab the best paper

### Related Essays

Personal statement for UK universities: born in Moscow and moved to Vienna
I have always wanted to pursue my career as a businessperson. I believe that whole of the world is under the control of the corporate world. Within this corporate world, there is a great demand for business students. The corporate world is extremely competitive, and educated people have an advantage over others, especially for the management of the business.
4 pages (1000 words) Essay
Problem
Why to spend time pondering over rather than resolving it? Not a single problem is irresolvable. It’s just our mind, way of thinking and intention to solve a problem which can guide us. To solve a problem appropriately, one must consider better options than escaping from it.(R.Sharf 18) Avoidance is not a solution; it is basically a quick move towards a more challenging situation.
2 pages (500 words) Essay
Getting Rid of the Federal Reserve Bank would Solve America's Problem
The foreclosure of financial institutions, increased cost of living, unemployment, among other factors has characterized the economic situation in America. Presidential politics is quite sensitive because it touches on policies that will influence the lives of America in the future.
5 pages (1250 words) Essay
Administration Management Outline 1. Introduction 2. Scope 3. Change Management Process 4. Change Request 5. Risk Management 6. Communication 7. Applicable Legislation 8. Work Break down 9. Project Schedule 10. Project Budget 11. Resource Allocation 1. Introduction Our client company Brendan Murphy intends to landscape the garden of his home in Dandenong Ranges.
3 pages (750 words) Essay
Operation Pressure Point.The Drug Trade Problem
The drug trade is very much alive in the streets of New York. According to the Drug Enforcement Agency, NYC is home to numerous drug trafficking organizations which cater to the diverse population and "source for organizations that smuggle drugs to other East Coast destinations and to Canada and Europe".
4 pages (1000 words) Essay
Sports in Culture
On the other hand, it offer' reflection' on the place of all thi' fighting in Renai''ance cultural and 'ocial life -- a very large place, Anglo argue', to which hi'torian' have not given 'ufficient attention. He include' art hi'torian' in the complaint; and one merit of the book i' to 'how the intere't that contemporary arti't' had in depicting fighting, mainly to illu'trate printed training manual'.
10 pages (2500 words) Essay
What is the problem with immigration, and how do we solve it
One of the major critiques that those opposing immigration employ to support their view is the sight that immigrants are grounds to unemployment and inferior wages for the actual
5 pages (1250 words) Essay
Getting rid of the Federal reserve bank would solve americas problem
Presidential politics is quite sensitive because it touches on policies that will influence the lives of America in the future. Sound policies in the economic sector would rejuvenate hope in America.
5 pages (1250 words) Essay
Qatar fencing federation organizational behavior and management
The whole management of the federation is inexperienced and the players are not only unavailable but do not put in any effort towards their performance hence poor results. There are four parties involved in the Qatar Fencing Federation issue, and they are the President, the
8 pages (2000 words) Essay
Applying a leadership theory to the Qatar Fencing Federation
There is a substantial lack of motivation and minimal team cohesion within the Qatar Fencing Federation. What the group requires, most primarily, is to become part of a unified team sustaining a set of norms, values and beliefs in which every group member becomes an active and valued contributor to the team and its goals.
4 pages (1000 words) Essay
Get a custom paper written
by a pro under your requirements!
Win a special DISCOUNT!
Put in your e-mail and click the button with your lucky finger