A rectangular field is to be covered by 800-meter of hog wire in such a way that one side has a river for its boundary. What should be the dimensions to achieve the maximum area?

Q: An open-top box is to be made from a 20 in by 30 in piece of cardboard by removing a square from…

A: Let each side of the square cut-off from each corner be x in. then the length of the base of the box…

Q: Find the length and width of a rectangle with a perimeter 160 and whose area is a maximum.

A:

Q: Using the side of a building as one side and fencing for the other three sides, a rectangular garden…

A:

Q: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with…

A: The area, A of a triangle is calculated using the formula: A=12×b×h, where b, h are the lengths of…

Q: A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum…

A:

Q: A wire of length 10 cm is divided into two parts which are bend in the form of  a  rectangle if it…

A:

Q: A manufacture wants to design an open box having a square base and a surface area of 256 square…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given 2300m of wire is used for fencing three sides and one side is covered by river

Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

A:

Q: A rectangular square-based open-top container is to be made so as the surface area equals 24 m2.…

A: let the dimensions of container according to question are :lengh=a,width=a, and height =hsurface…

Q: By cutting away identical square from each corner of a rectangular piece of cardboard and folding up…

A:

Q: A square piece of cardboard of side a is used to make an open-top box by cutting out a small square…

A: Since, a square piece of cardboard of side 'a' is used to make an open-top box by cutting out a…

Q: A farmer has 480 meters of fencing with which to build two animal pens with a common side as shown…

A:

Q: Find the dimensions of the rectangle of maximum area which can be laid out within a right triangle…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given: Length of wire for electric fencing is 2000 m, and one side of plot is bounded by a river. To…

Q: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

A: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

Q: 4) A farmer has 2000 feet of fence and wants to build a rectangular enclosure along a straight wall.…

A: Given:-rectangular fence along a straight wallthere is no fence along the walltotal length of…

Q: composed

A:

Q: A farmer has 600m of fence to enclose a rectangular divided pasture adjacent to an existing wall. He…

A: In question given that  farmer has 600m of fence to enclose a rectangular divided pasture adjacent…

Q: A farmer has enough money to build only 150 meters of fence. What are the dimensions of the field he…

A: We know that, The perimeter of a rectangle is 2l+b where l is the length and b is the breadth of the…

Q: Two hundred forty meters of fencing is available to enclose a rectangular playground. What should be…

A: Consider the given perimeter of the rectangle as P=240m

Q: Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a…

A: topic- application of derivatives

Q: A rectangular garden is to be constructed using a rock wall as one side of the g and wire fencing…

A: We are asked to find dimensions of the rectangle.

Q: Find two numbers whose sum is a, if the product of one by the cube of the other is to be a maximum.…

A:

Q: An open box is to be made from a square piece of material, 12 inches, by cutting equal squares from…

A: Here we use the concept of APPLICATIONS OF DERIVATIVES

Q: A rectangle is bounded by the x-axis and the semi-circle y = √(36 − x^2). What length and width…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A:

Q: a rectangular property has three sides fenced in against an existing river by 1,200 feet of wooden…

A: Consider the given information.

Q: A landowner wishes to use 2 miles of fencing to enclose a rectangular region of maximum area. 1.…

A:

Q: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

A: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

Q: A manufacturer wants to design an open box having a square base and a surface area of 244 square…

A:

Q: A package in the shape of a rectangular box can be sent by post as a postal order if the sum of its…

A: Solution by using Lagrange multipliers as follows :

Q: Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Determine the…

A: Application of derivative

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other sides by a…

A: Given a rectangular plot of farmland bounded by river on one side and fencing on other three sides.…

Q: A rectangular piece of paper has 28 square inches of print in it. If its top and bottom margins were…

A: Figure ( using given information ):

Q: from a piece of cardboard that is 24 cm by 48 cm ,cut equal squares out of the corners . fold up the…

A:

Q: A farmer has 1800 m of fencing to make two equal rectangular pens that share a common side.…

A:

Q: A rectangular chicken pen is bounded on one side by the wall of the house and the other three sides…

A: A rectangular chicken pen is bounded on one side by the wall of the house and the other three sides…

Q: Suppose that a pentagon is composed of a rectangle topped by an isosceles triangle. If the length of…

A: We have to find the maximum area.

Q: A piece of cardboard is 14 inches by 10 inches and the corners were to be cut out and fold up the…

A: Let squares of x inches will be cut from the corners.So the length of the…

Q: A farmer is is building a fence to enclose a rectangular area against an existing wall, shown in the…

A:

Q: With only 600 m2 of materials, a closed cylindrical tank is to be made. What should be the height of…

A: Let's find.

Q: What is the maximum area he can enclose?

A:

Q: An open box is to be made from a square piece of material by cutting equal squares from each corner…

A:

Q: A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from each…

A:

Q: A rectangular enclosure is built against a wall, which forms one side of the enclosure. If there is…

A: Let 'x' be the width of rectangular enclosure and 'y' be the length of rectangular enclosure.

Q: A farmer wishes to fence off a rectangular sheep pen and uses all of 100 m of fencing. An adjoining…

A: A farmer wishes to fence off a rectangular sheep pen and uses all of 100 m of fencing. An adjoining…

Q: A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals. What…

A:

Q: find the maximum volume of a rectangular box that a post office will accept for delivery of the sum…

A:

Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

A: