A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see the figure below). Find the dimensions of a Norman window of maximum area if the total perimeter is 28 feet.

Q: Suppose that 208 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given:  208 ft of fencing is used to enclose a coral From given figure diameter of the semicircle is…

Q: An expecting mother wants to convert a corner of the nursery in her house into a rectangular playpen…

A: Let x and y be the dimension of the rectangular playpen. Given

Q: A rectangular table has an area of 27ft? and a perimeter of 24ft. What are the dimensions of the…

A: Given that, A rectangular table has an area of 27 ft2 and a perimeter of 24 ft.

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. Find the dimensions of a…

A: A Norman window has the shape of a rectangle surmounted by a semicircle. This implies that the…

Q: An open-top box with a square base is to have a volume of 32 cubic feet. Find the dimensions of the…

A: To determine the dimension of the box which minimize the amount of material used.

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A: This question can be solved using the concept of maxima and minima.

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A:

Q: A 20 ft long water trough has ends in the form of isosceles triangles whose equal sides are 4 ft…

A:

Q: A rectangle has a perimeter of 112 ft then the dimensions of the rectangle with maximum area is a)…

A:

Q: A farmer wants to fence a rectangular field and then divide it in half with a fence down the middle…

A:

Q: A box with an open top is to be constructed from a square piece of cardboard 2m inches wide, by…

A: Given information: A box with an open top is to be constructed from a square piece of cardboard 2m…

Q: The base of a right prism is a rectangle. If the rectangle has dimensions 2 x 3, and the prism has a…

A:

Q: Find the dimensions of a rectangular prism whose volume is (x4 ‒  y4) units3.

A: Given that,                volume, v =  (x4 ‒  y4) units3

Q: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r

A: Let the length of the rectangle be 2x and the width of the rectangle be y. From the figure, the…

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 rectangle with sides measuring x in. and 4x-1 in. has an area of 663in.^2. What are the dimensions…

A:

Q: When the radius of a sphere is doubled, the volume of the new sphere is as large as the volume of…

A: The new radius is 2r now, So, the new volume will be: V=43π(2r)3=43π(8r3)=843πr3=8(old volume)

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

A: Given;

Q: A box with an open-top has a square base and four sides of equal height. The volume of the box is…

A:

Q: An architect designed a semicircular tunnel so that two trucks can pass each other with a 3-foot…

A: Let radius of semicircular tunnel be r, then its diameter will be 2r. Given: Height of truck=12…

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

A:

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins.  What…

A: Given volume of the can is (128)πcm3 Let height=h radius=x

Q: Suppose that 465 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: We are given that 465 ft of fencing is used to enclose a corral in the shape of a rectangle with a…

Q: If the length of three sides of a trapezium other than the base are equal to 10cm, then find the…

A:

Q: Suppose that 477 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that: Length of total fencing =477ft                             NOTE: As per our answering…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

A: Let's find.

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

A: Rectangle

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A:

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

A:

Q: A carpenter is building a rectangular room with a fixed perimeter of 392 ft. What dimensions would…

A: Let l & b be the length and breadth of the room

Q: what is the maximum possible volume of rectangle box with the sum of it is 12 edges 24cm

A:

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

A:

Q: A square piece of green origami paper that is 6 inches on a side is being made into a gift box (with…

A: Maximizing the surface.

Q: Suppose that 404 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Area of the shape=Area of the semicircle+Area of rectangle .Area of semicircle=πx22x12…

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

A:

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

A: To find the maximum possible volume of the box in cubic inches

Q: Three sides of a trapezoid are 8 inches in length. How long must the fourth side be, so that the…

A: Given: Three sides of a trapezoid are 8 inches in length. Let the fourth side of trapezoid be 8+2x…

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 dimensions of a rectangle with a perimeter of 120 ft that has the largest possible area.

A:

Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of a Norman…

A: The point where the function will be maximum can be obtained by differentiating the function and…

Q: A rectangle has a perimeter of 14 ft then the dimensions of the rectangle with maximum area is a)…

A: Perimeter of a rectangle is given by P=2(l+b), where l is length and b is breadth. Since the…

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

A:

Q: Find the dimensions of a rectangle with area 1728 m whose perimeter is as small as possible. (I both

A: Length of rectangle = 24√3 m  Width = 24√3 m

Q: The sum of the dimensions of a box with a sqaure base is 48 m. Find the maximum volume of the box.

A: Volume

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

A:

Q: Find the dimensions I x w of a rectangle with area 850yds. whose perimeter is as small as possible.…

A: