You have 120 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

Q: You have 1000 feet of fencing to construct six corrals, as shown in the figure. Find the dimensions…

A: Available fencing = 1000 ft∴ 4y+3x = 1000⇒ y = 1000-3x4   ---(1)Area enclosed , A = xy⇒A = x1000-3x4…

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: You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle…

A: Given Data The circumference of the rectangular region is C=80 yards.   Consider the length and…

Q: Farmer Ed has 500 meters of fencing, and wants to enclose a rectangular plot that borders on a…

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Q: Farmer Dan has 24 feet of fencing. He is going to build a rectangular pen and use natural-number…

A: Given fencing leanth. 24 feet

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

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Q: You have 50 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle…

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Q: David has 40 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle…

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Q: Farmer Ed has 900 meters of fencing, and wants to enclose a rectangular plot that borders on a…

A: Area = length x widthArea=A= x(900-2x)

Q: A rancher has 1000m of fencing to enclose three rectangular corrals. The corrals have the same…

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Q: You have 268 feet of fencing to enclose a rectangular region find the demensions of the rectangle…

A: let x is length, y is the width of  a rectangle  then Area          =x×y Perimeter =2(x+y)

Q: The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions f the…

A: Given that: Sum of perimeter of an equilateral triangle and a square is 10

Q: You have 176 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle…

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Q: The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the…

A: Given,          The back of Jill's property is a creek. Jill would like to enclose a rectangular…

Q: A canvas wind shelter for the beach has a back, two square sides, and a top. If 96 square feet of…

A: Given :           Let x be the length, and y be the width and height             Volume = xy2Surface…

Q: A FARMER WITH 200 M OF FENCE PLANS TO ENCLOSE A RECTANGULAR PIECE OF LAND USING A RIVER ON ONE SIDE…

A: Please refer the attached image for complete solution. THANK YOU.

Q: You have 300 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle…

A: Perimeter of a rectangle (P)=2(l+b)where l=length and b=breadthSubstitute…

Q: An architect is asked to design a game room in the shape of an isosceles trapezoid where the non…

A: Let's find fourth side length for maximum area.

Q: A track-and-field playing area is in the shape of a rectangle with semicircles at each end. See the…

A: Given that, A track-and-field playing area is in the shape of a rectangle with semicircles at each…

Q: Farmer Ed has 150 meters of​ fencing, and wants to enclose a rectangular plot that borders on a…

A: Given perimeter of fencing = 150 meters w = x  l = 150 - 2x   we know area of rectangle = length*…

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 gardener wants to enclose the area outside of his house for his plants and flowers. One side will…

A: topic - application of derivatives

Q: Consider a rectangle that has a perimeter of 40 inches. What are the dimensions (width and length)…

A: Given perimeter of rectangle=40 inches

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 49…

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Q: The perimeter of a rectangle is to be no greater than 80 centimeters and the width must be 10…

A: let length be x and width is given to be 10. Perimeter of a rectangle is defined as 2(length +…

Q: You have 100 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle…

A: Consider the given perimeter of the rectangle P=100yards As we know the perimeter of the rectangle…

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: A farmer wants to build a rectangular pen with 80 feet of fencing. The pen will be built against the…

A: Ans One side of reactangular pen is the wall of the       barn , let the length be 'x'.Opposite side…

Q: The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the…

A:

Q: The area of a rectangle is represented by 12x - x² where x is a side of the rectangle. For what…

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Q: The area of a rectangle is 12 square inches.  Find the dimensions of the rectangle such that the…

A: To determine the dimensions of the rectangle of maximum perimeter.

Q: a rancher has 720 feet of fencing to construct six corrals, find the dimensions that maximized the…

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Q: A gardener is building a garden shaped like a rectangle. If he has 100 meters of fencing to go…

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Q: David has 40 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle…

A: Let x and y be the one sides of rectangle.                          2(x+y)=40  (given)…

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 farmer has 480 meters of fencing with which to build two animal pens with a ... common side as…

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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: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.…

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Q: maximum possible area of the corral?

A: We can solve this problem in two manner. By considering as a simple arithmetic problem and also as…

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: Four feet of wire is to be used to form a square and a circle. How much of the wire should be used…

A: We have given the length of a wire 4 ft that is used to make square and circle;

Q: Find the dimensions of the rectangle in the figure shown below that will give the maximum area, if…

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Q: A farmer decides to enclose a rectangular​ garden, using the side of a barn as one side of the…

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Q: You are going to mark out a rectangular area with rope and divide it into smaller areas. One side of…

A: Given information: A rectangular area is divided by ropes into smaller parts. One side of the larger…

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

A: Let us assume that both pens have same dimensions.

Q: Find the dimensions of a rectangle of maximum area having a perimeter of 36 feet

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Q: The back of Jake's property is a creek. Jake would like to enclose a rectangular area, using the…

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Q: The base of a triangle measures 40 inches minus twice the measure of its height. For what measure of…

A: Let h is the height of the triangle Then, according to question  base=40-2h Then…