Show that a 6 × n board (n ≥ 2) can be tiled with L-shaped tiles, without gap and overlapping. Each L-shaped tile covers three squares.

Q: Show that among all rectangles with an 8-m perimeter, the one with largest area is a square.

A: Let l be the length and b be the breadth of the rectangle.

Q: A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees pläntec…

A: Given 24 trees per row1235 trees to plant

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Consider x to be the length and y to be the width of the rectangular region as shown below.

Q: Find the dimensions of a rectangle with area 1,331 m2 whose perimeter is as small as possible. (If…

A: Area of a rectangle is 1331 m2, whose perimeter is small as possible.

Q: Show that of all the rectangles with a given perimeter,the one with greatest area is a square.

A: Let the perimeter P is given.  Let, length = x and width= y So, 2(x+y)=P Or, x+y=P/2 Or, y= (P/2) -…

Q: Prove that of all rectangles with given perimeter, the square has the greatest area.

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Q: What two nonnegative real numbers a and b whose sum is 23maximize a2 + b2? Minimize a2 + b2?

A: Given that real number a and b whose sum is 23ie   a+b=23⇒b=23-a-1Let S be the sum of their…

Q: How many independent variables are there in a 10 x 2 x 6 x 2 factorial design?

A: Independent variables in 10×2×6×2.

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: . Bricks are stacked in 20 rows such that each row has a fixed number of bricks more than the row…

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Q: How many diagonals can you draw from one vertex in polygon with 35 sides

A: Given data: The given numbers of sides of the polygon are n=35. The expression for the numbers of…

Q: How many squares (of all sizes) are there on a standard 8x8 Chess board?

A: we have to find  how many squares of all sizes in 8*8 chess board ;

Q: Show that all the rectangles with a given perimeter , the square has the largest area

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Q: Show that of all rectangles with diagonal of length c, the square has the largest area.

A: using second derivative test to find if square has largest area.

Q: A rectangle is inscribed in a right triangle. If the triangle has sides of length 5, 12, and 13,…

A: Let x and y be the length and breadth of the rectangle inscribed in the triangle. Let us take the…

Q: A shipping company handles rectangular boxes provided the sum of the length, width, and height of…

A: Let the dims be x, y and z then volume V=xyz           -----------(1) and the restriction we have…

Q: Show that among all rectangles with a given perimeter, the square is the one with the maximum area.

A: A rectangle is a quadrilateral whose opposite sides are equal and parallel to each other. The…

Q: An open-topped box is constructed from a rectangula piece piece of cardboard that is twice as long…

A: An open-topped box is constructed from a rectangular piece of cardboard that is twice as long as it…

Q: 03) Find the largest by cutting volume of box with rectongular little squares no top out of the four…

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Q: Find the rectangle whose vertex is haveng on possible max comum area

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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: 5. Assume that each scoop can only hold a maximum of 8 pieces and a minimum of 2. How many ways are…

A:

Q: The new owner of an apartment wants to install a window in the shape of a rectangle surrounded by a…

A: Given:     Owner has total of 336 cm of wood frame.So the total parameter of the window…

Q: determine the sum of the measures of the interior angels of an octogon

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Q: Compute the area of the polygon with vertices at (6,1) (3,-10) (-3,-5) and (-2,0)

A: To Compute the area of the polygon with vertices at (6,1) (3,-10) (-3,-5) and (-2,0)

Q: Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as…

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Q: Suppose than an open box is to be made from a square sheet of cardboard by cutting out 3-inch…

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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: Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will…

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Q: 1.) How many sides does a polygon have if the maximum number of diagonals that you can draw inside…

A: ( As per Bartleby guidelines we are supposed to answer only one question at a time from a given…

Q: The Japanese game called Chu Shogi uses a square board. The board is covered with smaller squares…

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Q: 2. Use the fact that 12 oz is approximately 6.897 in to find the dimensions of the 12 oz Coke can…

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Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: How many small cubes with edge of 20 cm each can be just accomodated in a cubical box of 2 m edge

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Q: Is it possible to plant 10 trees in 10 straight rows with 3 trees in each row? Hint: Desargues says…

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Q: Suppose two squares of the same color are removed from an 8 x 8 chessboard. Is it possible to tile…

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Q: If the cube had only been rolled 50 times, how many times would you expect a shm GREATER than 9 to…

A: From the table, we see that the sum of greater than 9 rolled (11+4+3)=18 times. In the table total…

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Given problem:- A farmer is building a fence to enclose a rectangular area consisting of two…

Q: 4. Assume that each scoop can only hold a maximum of 8 pieces. How many ways are there to sprinkle…

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Q: Show that of all n-gons having the same perimeter, the regular n-gon has the greatest area. Show…

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Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

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Q: A 10ft board is to be cut into three pieces, two equal-length ones and the third 3 in. Shorter than…

A: Calculation:It is given that the length of a board is 10ft which has to be cut into three…

Q: If the farmer has 648 feet of fencing, what are the dimensions of the region which enclose the…

A: x = length of the rectangle y = width of the rectangle fencing =648 ft hence 2x + 3y = 648 x…

Q: What is the perfect square larger than 16?

A: This question is based on perfect square . If we consider just larger than 16 then our answer will…

Q: 4. Find the total areas of the shaded regions in (a) (b) y = xV4 – x² 2

A: Given: The shaded region as shown in figure: We have to find the area of the shaded region.

Q: An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with…

A: Given: an square box in which 64 square box (black and white)

Q: two diagonally opposite corners of a standard chessboard are removed. Is it possible to cover the…

A: Given that, Two diagonally opposite corners of a standard chessboard are removed. Every domino in a…

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

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Q: Find the area of the square whose side is 6x+ 3. 36 x2 + 36 X + 3 O6x2 O6x+36 X+9 O 36 x2 + 36 X + 9…

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