Find the area (in cm^2) of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 5 cm if two sides of the rectangle lie along the legs. _______cm^2

Q: A 40­inch board is to be cut into three pieces so that thesecond piece is twice as long as the first…

A: Let the length of first piece is x inches. The length of second piece is twice as long as the first…

Q: Find three consecutive even intergers such that the product of two smaller numbers is the same as…

A: Let the consecutive even integers be  x, x+2,x+4, where x  is even , then we use the given condition…

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

A:

Q: When the length of each side of a square is increased by 5 inches, the area of the resulting square…

A: area of square = side *side

Q: The loose-leaf version of the textbook for this course is being remade. The area of each page within…

A: The area ofeach page within which there will actually be print will be 32inches2, and eachpage will…

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

A: Total length of wire is =800 m It is given that A rectangular plot of  farmland will be bounded on…

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

A:

Q: An open-top box is to be made from a 30-inch by 54-inch piece of plastic by removing a square from…

A: Given:Dimension of plastic board=30inch by inch

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

A: Use property of equilateral triangle and rectangle to solve this

Q: Find the area of the largest rectangle that can be inscribed in a right triangle withe legs of…

A:

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

A: the triangle is an equilateral triangle. the length of one side is L.

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 rectangle garden has a circumference of 80mm. What is the maximum possible area of the garden?

A: Given: The perimeter of a rectangular garden is 80mm. A rectangle will have equal sides opposite to…

Q: a rectangular block of wood is x cm by (x+1) cm and (x+2) cm. Find the total surface area. What is…

A: The given dimensions of the wood is x by (x+1) by (x+2). Evaluate the total surface area as follows.…

Q: Find the dimensions of the rectangle of largest area having fixed perimeter 100.

A: Given: Perimeter of rectangle = 100.

Q: Find the area of the largest rectangle that can be inscribed ina right triangle with legs of lengths…

A: Let x and y be the length and width of the rectangle that is inscribed in a right triangle. The…

Q: The altitude of a right triangle that meets the hypotenuse at a right angle divides the triangle…

A:

Q: A city has a population of 9,435. Can the entire population fit onto the football field if the field…

A: Given: A city has a population of 9,435. The football field is 120 yards long and 75 yards wide.…

Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius 7

A: Consider the circle with radius 7 be, x2+y2=72x2+y2=49                         …1 Draw the figure of…

Q: A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to…

A: To find the dimensions of the largest field that can be enclosed with 800 feet of fencing

Q: Find the length x. 2.5 x, 4,

A: Solution: The objective is to find the length of x

Q: 1. Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3…

A: Given query is to find the dimensions of the rectangular corral

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: Find the area(square meters) of the largest rectangle that can be inscribed in an equilateral…

A: The rectangle is inscribed in an equilateral triangle of side 2 meters. The one side of the…

Q: The sum of the length and girth (perimeter of a cross-section) of a rectangular carried by a…

A: Look at the figure for the required package.

Q: Find the dimensions of the rectangle that'll give the max rectangle area, of perimeter of entire…

A: The perimeter of the entire figure is 12 feet.

Q: Find the greatest volume that a right circular cylinder can have if it is inscribed in a sphere of…

A: Here we have to find the greatest volume that a right circular cylinder can have if it is inscribed…

Q: A square with a side length of a= 6 inches, draw the golden rectangle with its dimensions and  find…

A:

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

A:

Q: Find the dimensions of a rectangle of area 256 ft that has the smallest possible perimeter. shorter…

A: Area= length * width Perimeter=2(length + width)

Q: Proctice Completina th 2x716x+9=| ニ1

A: Given that: x2+6x+9=1

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: 2. mzR+ mS+ mzT= 105° +x= +x = 42 X =

A: We have the given figure as

Q: An open-top box is to be made from a 12-inch by 18-inch piece of plastic by removing a square from…

A: We can find the value of x by using the second derivative test.

Q: A square with a side length of 5 inches, out of each corner, squares of side length 1 inch are cut…

A: Given that, A square whose side length is 5 in.Cut out a square from each corner whose side is 1…

Q: A rectangular box is to be made from a square piece of cardboard of side length 10 inches by cutting…

A: We need to determine dimension of box.

Q: the area of the squares are growing by 1 square unit. determine the side length of each square

A: the side length of each square is determined as shown below

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area Perimeter:…

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Q: x 2 - - 14x +33 Evalvate the indeter minate integrel

A:

Q: A 50-in. piece of wire is divided into two pieces and each piece is bent into a square. How should…

A:

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: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius 6…

A: Please refer the attached image for complete solution.

Q: A rectangular piece of fabric has a square cut out of one corner. The longer edge of the piece of…

A: Given, A rectangular piece of fabric has a square cut out of one corner. The longer edge of the…

Q: An open-top box is to be made from a 12-inch by 42-inch piece of plastic by removing a square from…

A:

Q: Determine the dimensions of the rectangle with perimeter 265 cm and maximum area.

A:

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: The ball dropped from a height of 10 meters bounces 2/3 of the previous one in each bounce. What is…

A: Total distance traveled by the ball; The ball drops from 10 meters; and bounces to 2/3*10 meters and…

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

A: