Find the dimensions of the rectangle of maximum area which can be laid out within a right triangle with legs 8 and 24 so that two sides of the rectangle lie on the legs of the triangle.

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

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Q: Find two positive integers whose sum is 16 and the sum of whose squares is minimum

A: Given sum of two numbers are 16. Let first number be x and second number=16-x. Now, sum of squares…

Q: A farmer needs to take a rectangular plot of land and divide it into 6fields of equal area. He has…

A: First of all, construct the diagram as per the question.Let, l = length of the field. b = breadth…

Q: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with…

A: The area, A of a triangle is calculated using the formula: A=12×b×h, where b, h are the lengths of…

Q: A wire of length 10 cm is divided into two parts which are bend in the form of  a  rectangle if it…

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Q: By cutting away identical square from each corner of a rectangular piece of cardboard and folding up…

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Q: Among all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What…

A: Two numbers having sum 16 We need to find all pairs of numbers having sum 16 and whose product is as…

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 field bordering a straight stream is to be enclosed. The side bordering the stream is not to be…

A: Consider x as the width of the rectangular field. Given that, 1000 yards of fencing materiel has…

Q: 4) A farmer has 2000 feet of fence and wants to build a rectangular enclosure along a straight wall.…

A: Given:-rectangular fence along a straight wallthere is no fence along the walltotal length of…

Q: A farmer has 600m of fence to enclose a rectangular divided pasture adjacent to an existing wall. He…

A: In question given that  farmer has 600m of fence to enclose a rectangular divided pasture adjacent…

Q: A farmer wants to build a riding arena in the shape of a rectangle topped by two semicircles. Find…

A: If you like the solution then please give it a thumbs up.. The Answer is:      Maximum Area = 160652…

Q: Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a…

A: topic- application of derivatives

Q: A rectangular garden is to be constructed using a rock wall as one side of the g and wire fencing…

A: We are asked to find dimensions of the rectangle.

Q: A courier service will deliver a package only if the length plus girth does not exceed 96 inches.…

A: NOTE: Refresh your page if you can't see any equations. . length L=x width W=x height H=y the…

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: An open box is to be made from a square piece of material, 12 inches, by cutting equal squares from…

A: Here we use the concept of APPLICATIONS OF DERIVATIVES

Q: A rectangle is bounded by the x-axis and the semi-circle y = √(36 − x^2). What length and width…

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

A: Given query is to find the attached maximum area inclosed by 800 meter wire l.

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 2 –…

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Q: a rectangular property has three sides fenced in against an existing river by 1,200 feet of wooden…

A: Consider the given information.

Q: A courier service will deliver a package only if the length plus girth does not exceed 96 inches.…

A: As per given  We have to determine dimension of rectangle box

Q: A rectangle is constructed with its base on the​ x-axis and its upper two vertices on the parabola y…

A: Given informationRectangle base is on x axisTop on parabola

Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 30 and with its…

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Q: A poster must have 32 sq. in, of printed matter with margins of 4" each at the top and 2" at each…

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Q: A package in the shape of a rectangular box can be sent by post as a postal order if the sum of its…

A: Solution by using Lagrange multipliers as follows :

Q: Find the dimensions of the rectangle with maximum area that can be inscribed in a Semi - circle of…

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Q: A rectangle is constructed with its base on the diameter of a semicircle with radius of 26 and with…

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Q: Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Determine the…

A: Application of derivative

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

A: The Perimeter of rectangular field = 800 m Let length of field = x m Width of field = y m

Q: A farmer wishes to build a rectangular fence and has 800 meters of fencing material with which to…

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Q: A box with an open top is to be constructed from a square piece of cardboard that is 4 feet wide by…

A: Square piece of cardboard of 4 feet wide. Let x feet be cut off from each corner of the square piece…

Q: A 17 cm x 11 cm open rectangular box is to be constructed by cutting square corners out of a piece…

A: Let the sides of square be x cm then the dimensions of the box will be as follows Dimensions of box…

Q: 6. A square sheet of cardboard of side 12 in. square is used to make an open box by cutting out…

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Q: A courier service will deliver a package only if the length plus girth does not exceed 96 inches.…

A: Given:- A courier service will deliver a package only if the length plus girth does not exceed 96…

Q: A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If…

A: Rectangular area is to fenced from three sides and by wall to one side.

Q: A rectangular chicken pen is bounded on one side by the wall of the house and the other three sides…

A: A rectangular chicken pen is bounded on one side by the wall of the house and the other three sides…

Q: Of all rectangles with a perimeter of 10, which one has the maximum area? (Give the dimensions.)

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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: 1. Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle…

A: From the given problem:   Perimeter=P=1000 m   Let the length of the rectangle 'abcd' is 'X' and…

Q: Of all rectangles with a perimeter of 17, which one has the maximum​ area? (Give the​ dimensions.)

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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: What is the maximum area he can enclose?

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Q: Find the rectangle of the maximum area that can be inscribed in a right triangle with legs of length…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 –…

A: Given data: The given equation of the parabola is y=8-x2. The below figure shows a rectangle is…

Q: A rectangular enclosure is built against a wall, which forms one side of the enclosure. If there is…

A: Let 'x' be the width of rectangular enclosure and 'y' be the length of rectangular enclosure.

Q: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…

A: Given: A courier service will deliver a package only if the length plus girth does not exceed 108…