A farmer wants to make a rectangluar enclosure using a wall of a barn as one side and 160 ft of fence for the other 3. Find the maximum area.

Q: A campground owner has 1800m of fencing. He wants to enclose a rectangular field bordering a river,…

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Q: A rancher has 240 ft of fencing with which to build a rectangular corral alongside an existing…

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Q: A farmer buys 120 m of fence. He wants to make 2 cages of 4 rectangles with the same length for his…

A: Let x and y be the  length and width of cage respectively (equals to dimensions of rectangle) total…

Q: Find the minimum cost of a rectangular box that is three times as long as it is wide and which holds…

A: Given  that length is three times as long as width so let width be x then length will be 3x  let…

Q: A rectangular storage area is to be constructed along a side of a building. A security fence is…

A: Given  Take length of side parallel to building = y  length of side perpendicular to building = x…

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

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Q: A machinist in an engineering machine shop has ordered a sheet of plastic with dimensions of 5 m × 6…

A: Dimensions of plastic sheet = 5m×6m×50mm            Dimensions of door  = 3m×4m where Length of…

Q: Jim wants to build a rectangular parking lot along a busy street but only has 2,800 feet of fencing…

A: This question is related to application of derivative.

Q: A rancher has 260 ft of fencing with which to build a rectangular corral alongside an existing…

A: Given A rancher has 260 ft of fencingLet the length of rectangle=x ftand width of rectangle=y ft

Q: A semi-elliptical goblet has a depth of 4 inches and its round opening has a width of 3 inches. It…

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Q: A gutter having a triangular cross section is to be made by bending in the middle of a strip of…

A: Here is the solution of the given problem.

Q: A rectangle sheet of cardboard measures 16 cm by 6 cm . equal squares are cut out of each corner and…

A: We need to find maximum volume.

Q: We have a piece of cardboard that is 50 cm by 20 cm and we are going to cut out the corners and fold…

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Q: Jim wants to build a rectangular parking lot along a busy street but only has 1,600 feet of fencing…

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Q: A rectangular box having a square base and open at the top is to have a capacity of 16823 cc. Find…

A: Given; A rectangular box having a square base and open at the top is to have a capacity of 16823 cc.…

Q: Your client wants you to construct a rectangular family pool in front of the house with perimeter of…

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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: An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a…

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of…

Q: An open box is to be made of a piece of cardboard 10cm x 16cm by cutting equal squares out of the…

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Q: we have 27ft squared of material to build a box of maximum volume with a square base and no top.…

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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: An open-top crate is to be constructed with 54 ft2 of material available to use. The length of its…

A: Let width = x So, length = 2xLet height = hVolume of the crate = V = (x)(2x)(h)= 2hx^2

Q: We have 48 m² of material to build a closed box whose base width is 2 times the base length. What is…

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

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Q: What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 14…

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Q: A 63-inch by 168-inch pieceof cardboard is used to make an open-top container by removing a square…

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Q: Glenview Community College wants to construct a rectangular parking lot on land bordered on one side…

A: Given : Let x be the width of the lot, and 380-2x be the length.  The area of the rectangular is…

Q: Find the minimum cost of a rectangular box of volume 180 cm³ whose top and bottom cost 4 cents per…

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Q: A box with an open top is to be constructed from a square piece of cardboard that is 4 feet wide by…

A: Square piece of cardboard of 4 feet wide. Let x feet be cut off from each corner of the square piece…

Q: We have 36ft2 of material to build a box of maximum volume with a square base and no top. What is…

A: To find the dimension of the square base for the optimum volume

Q: Suppose an open box with a rectangular base is to be constructed from a rectangular piece of…

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Q: A farmer wants to fence in two rectangular corrals, equal in area, using an inner fence as shown in…

A: Given;

Q: Paula plans to build a rectangular closure for her dogs using 140m of fencing. What is the maximum…

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Q: Phil wants to design an open box with a square base with a surface area of 400 square inches. What…

A: We need to find dimensions of a box whose volume is maximum.  & volume = x^2 y

Q: The base of an aquarium (in the shape of a cuboid) with given volume V is made of slate and the…

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Q: A rancher has 240 ft of fencing with which to build a rectangular corral alongside an existing…

A: We know, in rectangle, pair of opposite sides are equal.In rectangular corral, let length of equal…

Q: The volume of a box without a top is 36 m3, where the length is twice of width. Find the dimensions…

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Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Given: The total perimeter is 16 feet. The given window is formed by adjoining semicircle to the top…

Q: The size of the rectangle that can be made from 200 cm long wire so that the area is maximum is ….

A: We have to find the maximum area of given rectangle.

Q: A piece of wire 10 m long is cut into two pieces. One pieceis bent into a square and the other is…

A: To find: The way to use the wire such that the area enclosed by the triangle and square would be…

Q: A farmer has 20 feet of fencing, and he wishes to make from it a rectangular pen for his pig Wilbur,…

A: Let, width= x, length = y So, total fence needed= 2x+y=20 feet  y= 20-2x

Q: Find the dimensions of the rectangular box, open at the top, which has a minimum surface area if the…

A: Let us consider the width, length and height of the rectangular box are x, y and z respectively.…

Q: Find the minimum cost of a rectangular box that is three times as long as it is wide and which holds…

A: Consider the dimension of rectangular box be x, 3x, and h. Then, volume is given by V=x×3x×h  =3x2h…

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

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Q: A close rectangular box where length is double its width has a total surface of 300 square inches.…

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Q: A rancher has 244ft of fencing with which to build a rectangular corral alongside an existing fence.…

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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…

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Q: A company needs to build a warehouse with perimeter 300 ft. Find the dimensions to give maximum…

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

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