Without using a computer or a calculator, estimate the change in length of a space diagonal of a box whose dimensions are changed from 200×200×100 to 201×202×99.

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Q: Find the greatest volume of a rectangular box such that the sum of its length, width, and height…

A: Since you have posted multiple questions, I will solve only the first one as per the policy of…

Q: Determine the Maximum area of a rectangle lot that can be created with a 1000m length of fencing…

A: Given: Length of fencing is 1000m We know that fencing means boundary Let x, y be the length and…

Q: Find the dimensions of a rectangle with area 1000m2 whoseperimeter is as small as possible.

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Q: Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. Show…

A: Given:Perimeter of a rectangle is 68 m.

Q: Consider a sheet of metal in the form of a right triangle with base 36 inches and height  20 inches.…

A: Consider a sheet of metal in the form of a right triangle with base 36 inches and height 20 inches…

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Q: A farmer builds a rectangular grid of pens with 1 row and 5 columns using 550 feet of fencing. What…

A: Given problem:- A farmer builds a rectangular grid of pens with 1 row and 5 columns using 550 feet…

Q: A box with a square base and with height is to be constructed so that it has a volume of 1000 cubic…

A: A box with a square base and with height is to be constructed so that it has a volume of 1000 cubic…

Q: Show that the rectangle which has maximum area for a given perimeter is a square.

A: This problem can be solved by expressing the area of the rectangle as a function of single variable…

Q: A farmer plans to use 180 feet of fencingto enclose a rectangular region, using part of a straight…

A: Given:A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a…

Q: A piece of wire 60 cm long is to be folded into a rectangle.what should be the dimensions so that…

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Q: According to postal regulations, a carton is classified as “oversized” if the sum of its height and…

A: Assume a be the side length of the square base,h be the height of the carton and V be the volume of…

Q: Find the area of the largest rectangle that can be inscribed in an equilateral triangle of side…

A: Given: A rectangle inscribed in an equilateral triangle of side L assuming one side of the rectangle…

Q: 28, g6) = 2x2 [,3],8 reclanyles

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Q: What are the dimensions of a rectangular wall that can be constructed with 81 feet of brick that…

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Q: Norman builds a rectangular pig pen with two parallel partitions using 150 meters of fencing…

A: let the length of Pig pen be "a"width be " b" Perimeter=150 metresPerimeter = 2(a+b)…

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

A: Modelling the problem: Let the three dimension be x, x and y .Since base is a square base.   also…

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

A: Area of a rectangle with length x and breadth y is given by x.y. Perimeter of a rectangle with…

Q: If 1800 feet is available to build 5 adjacent pens, find the dimension of the pens that will…

A: Given:The perimeter of all 5 pens is 1800 ft.Calculation:Let x and y be the length and thge width of…

Q: Suppose a rectangular picture frame has a thin border made from a 144-inch-long strip of bronze. If…

A: # Considering the width of border negligible Length of the strip is 144 inch Now let the length of…

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

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Q: Find the dimensions of a rectangle with a perimeter of 160 ft that has the largest possible area.…

A: Perimeter of a rectangle=2l+bArea of a rectangle=length×breadthGiven: Perimeter = 160

Q: A rectangular field is four times as long as it is wide. If the perimeter of the field is 500 yards,…

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Q: One side of an open field is bounded by a straight river. Determine how to put a fence around the…

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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: Let x be the width and y be the length of the rectangle.From the given statement, the three side…

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

A: Given  Total length of the fence=2500 m Letl=length of the plotb=width of the plot

Q: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

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: A farmer has 400 ft of fencing with which to enclose a rectangular field adjacent to anexisting…

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Q: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral…

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

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Q: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius 10. *

A: From the given figure we can derive length and breadth. below are the steps.

Q: An open-typed rectangular box is to be made from a piece of cardboard 24 cm long and 9 cm wide by…

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Q: What are the dimensions of the rectangular field of maximum area that can be fenced with exactly 500…

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Q: Determine the dimensions of the rectangle of rectangle of the largest area that can be inscribed in…

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Q: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral…

A: Let base of the rectangle = 2x and height = y

Q: A farmer with 750 ft of fencing wants to enclose a rectangular region and then divide it into four…

A: Solve for the lager rectangle dimension and area of large rectangle

Q: What are the dimensions of a rectangle that will maximize the area given its imeter is 100 units?

A: Given: Perimeter of rectangle is 100 units   To Find: Dimensions of a rectangle that will maximize…

Q: A 27-inch by 72-inch piece of cardboard is used to make an open-top box by removing a square from…

A: The numerical is interpreted as shown in the drawing below;

Q: The owner of the Rancho Grande has 2,972 yd of fencing with which to enclose a rectangular piece of…

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Q: Find the dimensions of the rectangle of largest area that canbe inscribed in an equilateral triangle…

A: Solution:- We have to find the  dimensions of the rectangle of largest area that canbe inscribed in…

Q: A Photo Paper with margins of 1.00 inch at the top and bottom and 1.50 inch at the sides is to…

A: Let x and y be the width and length of the page (measured in inches). Given that the area of print…

Q: A farmer plans to use 180 feet of fencingto enclose a rectangular region, using part of a straight…

A: The fencing used is 180 feet. The fencing has three side and one side is the river bank. Given that,…

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

A: Let a and b be the sides of a retangular fence.

Q: Find the dimensions of a rectangle of area 324 ft2 that has the smallest possible perimeter.…

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Q: 2. The area of a rectangular field is 162 sq. m and its length is twice its width. Find the…

A: Given,            Area of the rectangular field is 162 sq. m

Q: What are the dimensions of the base of the rectangular box of greatest volume that can be…

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