A rancher with 120 meters of fencing wants to enclose a rectangular region along a river. Find the length and width of the region and the maximum area that can be enclosed.  A) express the area of the region as a function of the length x of the side parallel to the river  what are the dimensions and what is the maximum area

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: A triangle has a base of (2 - x) cm and a height of (2x + 6) cm. What is the maximum area of the…

A:

Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A: We will use the basic knowledge of 3D solid geometry and applied differential calculus to answer…

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

A:

Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

A:

Q: A square piece of cardboard of side a is used to make an open-top box by cutting out a small square…

A: Since, a square piece of cardboard of side 'a' is used to make an open-top box by cutting out a…

Q: A rectangle sheet of cardboard measures 16 cm by 6 cm . equal squares are cut out of each corner and…

A: We need to find maximum volume.

Q: An open-top box is to be made from a 36 in. by 27 in. piece of cardboard by removing a square from…

A:

Q: Your client wants you to construct a rectangular family pool in front of the house with perimeter of…

A:

Q: A farmer wants to secure a certain part of his land. Calculate the maximum area of a rectangular lot…

A: Given: total length of fencing material of rectangular plot = 1000m

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 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: the maximum area of a rectangle inscribed in a semicircle  of radius 5 inches if its base lies along…

A: Consider the given information as The maximum area of a rectangle inscribed in a semicircle  of…

Q: Calculate the total area of the semiregular polyhedron of the image knowing that its edge is a.…

A: We can find the answer as below.

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

A:

Q: An open box is constructed by cutting square corners with side x cm from a 150-cm by 100-cm sheet of…

A: According to the problem, we have

Q: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

A: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

Q: 1. Assuming that one of the sides of a rectangular field is along a river bank and no fencing is…

A: In this question, we want to know the dimensions of the rectangular field that will satisfy the…

Q: two chicken coops are to be built adjacent to one another from 144ft of fencing. WHAT DIMENSIONS…

A: Let the length of the individual chicken coops = x ft Let the width of the individual chicken…

Q: A rectangle is bounded by the x-axis and the semicircle y=sqrt(81-x^2) what length and width should…

A: Given that A rectangle is bounded by the x-axis and the semicircle y=sqrt(81-x^2) To find what…

Q: A rectangular playing field is to have an area of 400 sq. meters. Fencing is required to enclose the…

A: Concept: Area of the rectangle is  A=length×width Fencing of the rectangle means covering its…

Q: A one compartment vertical file is to be constructed by bending the long side of an 8 in. by 14 in.…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other sides by a…

A: Given a rectangular plot of farmland bounded by river on one side and fencing on other three sides.…

Q: What is the maximum area of atriangle which is in scribed in acircle of radius 4cm and one of its…

A:

Q: What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval…

A:

Q: from a piece of cardboard that is 24 cm by 48 cm ,cut equal squares out of the corners . fold up the…

A:

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

A:

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: Find the dimensions of a rectangle of maximum area inscribed in a circle of radius 4. (Must show…

A: Let ABCD be the rectangle inscribed in the circle of radius 4. AC and BD are the diameters of length…

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

A:

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

A: Let the length of the portion of the wire to form a square is x, then the length of wire to form a…

Q: A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions…

A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So,…

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…

A:

Q: A rectangular piece of cardboard has a size of 45 x 24 cm. This cardboard will be made into a box…

A:

Q: An open box is to be constructed from a 12x12-inch piece of cardboard by cutting away squares of…

A: Let the cut away squares side is of x in. So, the dimension of the open box with height x, length…

Q: The size of the rectangle that can be made from 200 cm long wire so that the area is maximum is ….

A: We have to find the maximum area of given rectangle.

Q: Using the side of a building as one side and fencing for the other three sides, a rectangular garden…

A: Given: Using the sides of a building as one side and fencing for the other three sides,a rectangular…

Q: A piece of wire of length 200 ft is bent into the shape of a rectangle. Which dimensions produce the…

A: Given:  Length of wire = 200 ft Wire is bent into the shape of a rectangle So, perimeter of…

Q: A parcel delivery service will deliver a package only if the length plus the girth (distance around,…

A: Let the side of the rectangular box is l, b and h.  Maximum possible dimension is  2l + 2b + h = 108…

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

A:

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: A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from each…

A:

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

A:

Q: A farmer wishes to fence off a rectangular sheep pen and uses all of 100 m of fencing. An adjoining…

A: A farmer wishes to fence off a rectangular sheep pen and uses all of 100 m of fencing. An adjoining…

Q: A printed page is to contain 60 cm2 of printed material (not including the margins) with margins (on…

A:

Q: A farmer wishes to enclose a rectangular region bordering a barn with fencing, as shown in the…

A: Assume the below figure top be the given figure as mentioned in the question. Let the length of the…