The perimeter of a rectangle is 36 m. Use a calculus approach to determine the maximum area of such a rectangle.

Q: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The…

A: Here we have to find the length and width of the rectangle that has perimeter of 32 with maximum…

Q: Determine the Maximum area of a rectangle lot that can be created with a 1000m length of fencing…

A: Given: Length of fencing is 1000m We know that fencing means boundary Let x, y be the length and…

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: Let the length of the rectangle = LLet the breadth of the rectangle = BPerimeter of the rectangle =…

Q: Find the maximum area of a rectangle circumscribed about a fixed rectangle of length 10cm and width…

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Q: A rectangular box with a square base is to be constructed from 1000 square inches of cardboard. Find…

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Q: Show that the rectangle which has maximum area for a given perimeter is a square.

A: This problem can be solved by expressing the area of the rectangle as a function of single variable…

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: A rectangle garden has a circumference of 80mm. What is the maximum possible area of the garden?

A: Given: The perimeter of a rectangular garden is 80mm. A rectangle will have equal sides opposite to…

Q: Of all rectangles with a fixed perimeter of P, which one has the maximum area? (Give the dimensions…

A: let the length of rectangle is l and width is bthen perimeter (P)=2(l+b)sol+b=P2or l=P2-b

Q: farmer has 600 feet of fencing with which to build a rectangular coral having two internal dividers…

A: Given, Total fencing= 600 feet Let x and y be the sides of the rectangular coral. y be the dimension…

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: A farmer would like to fence his rectangular lot on a river bank. If he has 800 m of fencing…

A: In the question consider the field as rectangular.  Let h be height of rectangle and b be breadth of…

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

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Q: An open box will be made by cutting a square from each corner of a 10-cm by 16-cm piece of cardboard…

A: To find: The size of square to be cut from the corner of cardboard to maximize volume and also find…

Q: с. How should the fencing be used to get the maximum possible area? How much area will the chickens…

A: Given that Total length of fencing wire is 100 ft to build the chicken coop. Since  marissa has to…

Q: A cardboard box without a lid is to have a volume of 4000cm3. Find the minimum amount of cardboard…

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Q: A rectangle has a perimeter of 40m. What could be the maximum area of the rectangle?

A: A rectangle has a perimeter of 40 m. Let x and y be the length and width of the rectangle. Now…

Q: What is the maximum total area of such a corral?

A: Let the length of rectangular corral = LBreadth of rectangular corral = BPerimeter of rectangular…

Q: A farmer wishes to enclose a rectangular region bordering a river, using 960 feet of fencing. What…

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Q: A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencng = 200 feetTotal fencing = 4x+3y=200 feet  — (i)Area = 2x×yFrom eqn - i - y =200-4x3Area…

Q: A rectangle has one corner at the point (0,0), a second corner on the posit below. What is the…

A: Let the length of the rectangle be "y" and breadth be "x". The expression for the area of the…

Q: If a closed tin can of volume 16x cubic inches is to be in the form of a right circular eylinder,…

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Q: A rectangular box without a lid is to be made from 12m2 of cardboard. Find the maximum volume of…

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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: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: The given Perimeter P = 48 m Let length of rectangle l = x  Width = b

Q: A window is in the shape of a rectangle surrounded by a semicircle. If the perimeter of the window…

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Q: Of all rectangles with a perimeter of 10, which one has the maximum area? (Give the dimensions.)

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Q: A box with no top has a square base. If 64 squared centimeter of material is used, what is the…

A: A box with no top has a square base and 65 cm^2 of material is used

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: Find the maximum volume of a rectangular box with no top that has a surface area of 48 square…

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Q: When enclosing 4 sides, the maximum area for a given rectangular area is obtained by forming a ?…

A: Rectangle

Q: A manufacturer wants to design an open box having a square base and a surface area of 108 square…

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Q: Of all rectangles with a perimeter of 17, which one has the maximum​ area? (Give the​ dimensions.)

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Q: if the hypotenuse of a right triangle is 25, show that the area is a maximum of it is isosceles

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area Perimeter:…

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Q: WHAT IS THe MAXIMUM AREA ENCLOSED BY A RECTANGLE HAVING PERIMETER OF 52 INCHES?

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Q: A rectangular box without a lid is to be made from 12 m2 of cardboard. Find the maximum volume of…

A: Given that a rectangular box without a lid is to be made from 12 m² of cardboard.

Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: A rancher has 480 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencing needed in that given picture is= x+x+x+x+y+y+y=4x+3y Given that the rancher has 480…

Q: A fencing is limited to 50m length. What is the maximum rectangular area that can be fenced in using…

A: Recall:  Area of rectangle=length*breadth

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: A farmer has 3000 m if fencing on hand. Determine the dimensions of a rectangular fencing that…

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Q: A farmer has 1,200 feet of fence and wishes to build two identical rectangular enclosures, as in the…

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Q: A carpenter is building a rectangular room with a fixed perimeter of 116 ft. What dimensions would…

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

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