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

Q: The minimum surface area for a given volume of a square-based rectangular prism occurs when the…

A: Let us assume the length of a edge of the base=xAnd height =y And volume=VSo, V=x2yor, y=Vx2

Q: Show that among all rectangles with an 8-m perimeter, the one with largest area is a square.

A: Let l be the length and b be the breadth of the rectangle.

Q: A rectangular lot has a perimeter of 80m. If its lot area is to be maximized, what is its length? *

A: Let the Length of the rectangle be:  x Let the Width of the rectangle be: y It is given that the…

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: 3.) A fencing is limited to 50ft length. What is the maximum rectangular area that can be fenced in…

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Q: Show that of all the rectangles with a given perimeter,the one with greatest area is a square.

A: Let the perimeter P is given.  Let, length = x and width= y So, 2(x+y)=P Or, x+y=P/2 Or, y= (P/2) -…

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: Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of…

A: Solution:- calculate the value of base by using pythagores therorm.

Q: a. A rectangular pen is built with one side against a barn. If 400 m of fencing are used for the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Note: According to Bartleby guidelines; For more than one question asked only the first one is to be…

Q: Show that of all rectangles with diagonal of length c, the square has the largest area.

A: using second derivative test to find if square has largest area.

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

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Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: A…

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Q: Find the dimensions of a rectangular box of volume 1000cubic inches for which the sum of the…

A: Let x,y,z be the length, breadth and the height of the rectangular boxxyz=1000  and the sum…

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

A: Let the length of a rectangle is x  Let the width of the rectangle be y

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: A rectangular lot has a perimeter of 80m. If its lot area is to be maximized, what is its length?

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Q: 5. FIND THE MAXIMUM AREA FOR A RECTANGULAR ENCLOSURE USING 480 FEET OF FENCING MATERIAL AND…

A: I am attaching image so that you understand each and every step.

Q: A rectangular field is to be covered by 800-meter of hog wire in such a way that one side has a…

A: Area of a rectangle with length x and breadth y is given by x.y. Perimeter of a rectangle with…

Q: What are the dimensions of a rectangular wall that can be constructed with 100 feet of brick that…

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Q: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

A: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

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

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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: Use Lagrange multipliers to find the dimensions of a rectangular box with largest volume if the…

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Q: 2. Show that of all rectangles with diagonal of length c, the square has the largest area.

A: All rectangles with diagonal of length c, the square has the largest area.

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: what is the minimum perimeter that a rectangle with an area of 32 ft2 can have?

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Q: 5. Find the maximum area of an isOsceles triangle whose perimeter is 18 inches.

A: 5) To find out the maximum area of an isosceles  triangle whose perimeter is 18 inches.

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: 4-Find the length and width of a rectangle with perimeter 100 m that maximize the a

A: I have solved the 4th question for you since you have marked it. As per guidelines, we are supposed…

Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

A: Let x and y be the length and width of the rectangle inscribe in a circle of radius a. Then the…

Q: A fencing is limited to 120ft length. What is the maximum rectangular area that can be fenced in…

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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: Find the maximum area of a rectangle that can be circum -scribed about a given rectangle with length…

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Q: . A window consists of an open rectangle topped by a semicircle and is to have a perimeter of 288…

A: It is given that the perimeter, P of the window is 288 inches and we have to radius of semicircle…

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

A: Rectangle

Q: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral…

A: Let base of the rectangle = 2x and height = y

Q: What are the dimensions of a rectangle that will maximize the area given its imeter is 100 units?

A: Given: Perimeter of rectangle is 100 units   To Find: Dimensions of a rectangle that will maximize…

Q: Find the dimensions of a rectangle with area 100 m? whose perimeter is as small as possible? Find…

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: If the farmer has 648 feet of fencing, what are the dimensions of the region which enclose the…

A: x = length of the rectangle y = width of the rectangle fencing =648 ft hence 2x + 3y = 648 x…

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

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Q: Is the rectangle of fixed area whose perimeter is a minimum a square?

A: Given Area of a rectangle =  square units-----(1)   Let length of the rectangle be feet and the…

Q: The owner of a ranch has 1,000 yards of fencing material with which to enclose a rectangular piece…

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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: 4. Find the maximum area of an isosceles triangle inscribed in a circle of radius r.

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Q: Of all rectangles with area 64, which one has the minimum perimeter?

A: It is required to find the dimensions of rectangle having area 64 units which will have a minimum…

Q: Suppose an airline policy states that all baggage must be rectangular with a sum of length, width,…

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