2. A rectangular field of fixed area is to be enclosed and divided into five lots by parallel to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum

2. A rectangular field of fixed area is to be enclosed and divided into five lots by parallel to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.4: Cicumference And Area Of A Cicle

Problem 18E: A rectangle has an area of 36 in2. What is the limit smallest possible value of the perimeter of the...

See similar textbooks

Related questions

Q: The City Council proposed to utilize a government-owned Iand with an area of 21, 600 square meters.…

A: Part a

Q: The City Council proposed to utilize government-owned land with an area of 9,600 square meters.…

A: Given: The City Council proposed to utilize government-owned land with an area of 9,600 square…

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters.…

Q: The City Council proposed to utilize government-owned land with an area of 9,600 square meters.…

A: We have to find the minimum length of fencing required fro the mango plantation land. Give the…

Q: The City Council proposed to utilize a government-owned land with an area of 15, 000 square meters.…

Q: 12. Show that a rectangle with given perimeter has maximum area when it is a square.

Q: 7. A manufacture want to design an open box having a square base and a volume of 256 cm³. What…

A: Given problem is :

Q: 3. A piece of wire 36 in. is cut into two parts, one of which is bent into the shape of an…

Q: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters.…

A: Given that: The City Council proposed to utilize a government-owned land with an area of 15,000…

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters.…

Q: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters.…

A: IT IS GIVEN THAT TOTAL AREA OF THE LAND IS 15,000 M2AND ONE -THIRD OF IT WILL BE USED AS PICNIC AREA…

Q: As an Engineer, cite other instances aside from the situations given above where optimization (one…

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a 30°-60°-90° triangle and…

Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

Q: The government proposed to utilize a government-owned land with an area of 12,150 square meters.…

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters.…

A: (1) Given information: The area of land is 9600 square meters. One third area is used for the…

Q: The City Council proposed to utilize a government-owned land with an area of 21,600 square meters.…

A: Given:total area =21600m2land used for picnic=1/3 of the total land

Q: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters.…

A: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters.…

Q: The City Council proposed to utilize a government-owned land with an area of 21,600 square meters.…

A: the total area of land given to us is 21600 sq units one- third of the land is used for picnic i.e…

Q: The City Council proposed to utilize government-owned land with an area of 15,000 square meters.…

Q: From a tract of land, a developer plans to fence a rectangular region and then divide it into two…

A: Given: Cost of fence on outside = $20 per foot Cost of middle fence = $8 per foot Area of each lot =…

Q: The City Council proposed to utilize government-owned land with an area of 15,000 square meters.…

A: Here we solve the given problem of calculus.

Q: what is the minimum possoble perimeter for a rectangle whose area is 100 in^2

Q: 1. Assuming that one of the sides of a rectangular field is along a river bank and no fencing is…

A: In this question, we want to know the dimensions of the rectangular field that will satisfy the…

Q: The City Council proposed to utilize a government-owned land with an area of 15, 000 square meters.…

A: Let dimensions of area for mango trees be length = xwidth = yarea=13 of total…

Q: 2 2. A rectangular playing field is to have area 600 m . Fencing is required to enclose the field…

Q: 19. A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of…

Q: The City Council proposed to utilize a government-owned land with an area of 12, 150 square meters.…

A: Given: 12150 m2 = total land area of the city13rd area = For mango tree garden23rd area = For…

Q: A poster is to contain 300 cm? of printed matter with margins of 10 cm at the the top and bottom and…

A: Assume some variable to be length and breadth of the poster then find its area. Derivative of area…

Q: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters.…

A: The total area of land is 15,000 square meters. (1). From question Picnic Area= 150003=5000 m2 Let…

Q: The City Council proposed to utilize a government-owned land with an area of 9, 600 square meters.…

Q: A farmer wants to enclose a rectangular field with area 1,000 square meters by fencing it into four…

Q: olume 150 cm3 whose top and bottom cost 7 cents per cm2 and whose sides cost 9 cents per cm2. Round…

A: answer is in next step. please give a like !!

Q: 19. If the farmer in Exercise 18 wants to enclose 150 square meters of land, what dimensions will…

A: The minimum of a function can be obtained at the point where the slope of the function is 0. The…

Q: 1. Find the dimensions of a rectangular box with a square base and no top that has a volume of 100…

A: Solve By minimizing surface area

Q: The City Council proposed to utilize a government-owned land with an area of 9; 600 square meters.…

A: Total area = 9600 square meters, One-third of the area will be used to plant mango trees, it means…

Q: A triangle is formed by the positive coordinate axes and a straight line through (6,3) . How large…

Q: 4. A television manufacturing firm needs to design an open-topped box with a square base. The box…

A: Here we have to follow the steps according to the question information to get the answer so I'm…

Q: A company is constructing an open-top, square-based, rectangular metal tank that will have a volume…

A: Given:- A company is constructing an open-top, square-based, rectangular metal tank that will have a…

Q: The City Council proposed to utilize a government-owned land with a area of 15, 000 square meters.…

A: Given: The land has an area of 15,000 square meters. One-third of the area is used to plant mango…

Q: The City Council proposed to utilize government-owned land with an area of 15,000 square meters.…

A: Main land area is given 15000 square meters. One-third of the area will be used to plant mango trees…

Q: 1. A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to…

Q: 6. A soda company is designing a new can that is more cost efficient. The base of the can costs…

Q: 5., You are building TWO identical pens adjacent to each other with a total area of 100 m², as shown…

A: Let's solve 5th question, dimensions for minimize the amount of fencing.

Q: 2. Find the dimensions of a rectangle with an area of 108 square feet that has the minimum…

A: Area of rectangle = (length)*(width) = 108 sq. ft we need to find dimensions of a rectangle with…

Q: Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm…

A: Let the three sides or edges of the rectangular box be a,b and c in cm. Surface area of the box will…

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters.…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The City Council proposed to utilize a government-owned land with an area of 15,000 square meters.…

Q: 4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that…

A: West Coast Customs is constructing and open-top, square-based.rectangular subwoofer box that will…

Question

2. A rectangular field of fixed area is to be enclosed and divided into five lots by parallel
to one of the sides. What should be the relative dimensions of the field to make the
amount of fencing minimum

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

Step 10

Trending now

This is a popular solution!

Step by step

Solved in 10 steps with 10 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.
A rectangle has an area of 36 in2. What is the limit smallest possible value of the perimeter of the rectangle?
A wire b is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle. If the sum of the areas enclosed by each part is a minimum, what is the length of each part?
A piece of wire of length L is cut into two parts, one of which is bent into the shape of a square and the other into the shape of a circle. a.) How should the wire be cut so that the sum of the enclosed area is a minimum? b)How should it be cut to get the maximum enclosed areas?
Two cities A and B are 8 km and 12 km, respectively, north of a river which runs due east. City B being 15 km east of A. a pumping station is to be constructed (along the river) to supply water for the two cities. Where should the station be located so that the amount of pipe is a minimum?
A rectangular field is to have an area of This is to be enclosed and divided into three equal lots parallel to the shorter side. The minimum length of fencing material (including the partitions) is proposed. If we let y be the width,and 3x be the length, what is the minimum length of fencing material?
A water tank is to be constructed with a square base and open top, and is to hold 64 cubic yards. If the cost of the sides is $1 a square yard, and of the bottom $2 a square yard, what are the dimensions when the cost is a minimum? What is the minimum cost?
Consider a simple, homogeneous monocentric city with a circular shape. If the location rent premium at the center is $5,000 per year per acre, the rent at the edge of the city is $10,000 per year per acre, and the density is 2 persons per acre. Supposing that the annual transportation cost per person per mile of distance from the CBD is $200 (round-trip), and if the population increases by 10% (density and transportation cost do not change), what will be the new rent at the center of the city per year per acre? Please show how to calculate.
Find the maximum number of lines determined by n coplanar points.
ONLY parts L, M, and N please show work too
A triangle has variable sides x, y, and z subject to the constraint such that the perimeter is fixed to 18 cm. What is the maximum possible area for the triangle?
A rectangular field is to have an area of 900 sq. m. This is to be enclosed and divided into three equal lots parallel to the shorter side. The minimum length of fencing material (including the partitions) is proposed. If we let y be the width, and 3x be the length, what is P'(x)?