Show that among all rectangles with a given perimeter, the square is the one with 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: To calculate the least square, explain the conditions need to get satisfied?

A: Regression: Regression is a technique that is used to determine relationship between two or more…

Q: 5. A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: Let the length of the wire cut=xAll sides of square are same side length=yPerimeter= 4 y…

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 piece of wire of length 58 is​ cut, and the resulting two pieces are formed to make a circle and a…

A: Let the circle gets x units and the square gets (58-x) units x is from 0 to 58   Let radius of the…

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Consider x to be the length and y to be the width of the rectangular region as shown below.

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: Prove that of all rectangles with given perimeter, the square has the greatest area.

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Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

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

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

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Q: Three equally sized rectangular lots are enclosed by fencing the perimeter of a large rectangular…

A: Figure Three equally sized rectangular

Q: 5. Find the length and width of a rectangle that has an area of 32 square feet and a minimum…

A: Given, area A=32 sq.ft Let, x be the length and y be the width. The formula for the area of a…

Q: Show that all the rectangles with a given perimeter , the square has the largest area

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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: A wire of length 10 is to be cut into two pieces, one being bent to form a square and the other to…

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Q: 3. A farmer has 6000 m of fencing and wishes to create a rectangular field subdivided into four…

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

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Q: A piece of sheet metal is rectangular, 5 feet wide and 8 feet long. Congruent squares are to be cut…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the…

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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: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A: Using Lagrange multiplier to find the dimension of rectangle whose area is maximum

Q: Suppose that a homeowner wants to create a rectangular enclosure for his pet turkey in his backyard…

A: It is given that, the rectangle has one side of enclosure and fencing on other 3 sides. A total of…

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

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Q: 2. Find the length and width of a rectangle that has an area of 800 square feet and whose perimeter…

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

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Q: Consider the rectangle inscribed in a right triangle, in such a way that the rectangle sits in the…

A: Let, ABC be the right angled triangle with ∠C=90°, as shown in figure with rectangle DEFC…

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

A: the length of the square end edge is =?                                     box height is =? the…

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: What is the maximum volume of an open box that can be made from a square piece of cardboard, 10in on…

A:

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

A: We will use second derivative test to find the maximum volume.

Q: A rectangle with length L and width W is cut into four smaller rectangles by two lines parallel to…

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Q: Find the maximal area of a right triangle with hypotenuse of length 2.

A: Given:     Hypotheses length = 1

Q: 6] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

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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: A one-story building having a rectangular floor space of 13200 ft2 is to be constructed where a 22ft…

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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: Prove that among all rectangles with area 100 square units,the square has the smallest perimeter.

A: The area of the rectangle is defined as the product of length and breadth of the rectangle, whereas…

Q: A wire 12 inches long is cut into two, one part is bent in the form of a circle, and the other into…

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

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Q: )A wire of length L is cut into pieces, one being bent to form a square and the other o form an…

A: Given problem is :

Q: A farmer wants to construct a fence around an area of 7776 square feet in a rectangular field and…

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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: Find the area of a square whose diagonal has length V10 in.

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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…