The sum of the bases and altitude of a trapezoid is 36 inches and one base is 6 inches longer than the other. Find all three dimensions if the area is a maximum. Indicate also the maximum area.

Q: Find two numbers whose sum is a , if the product of one by the cube of the other is to be a maximum.

A: We have to find number

Q: The sum of the bases and altitude of a trapezoid is 36 inches and one base is 6 inches longer than…

A: We have to find all three dimensions

Q: Find the length and width of a rectangle taht has an area 968 square feet and whose perimeter is a…

A: Let x and y(in feet) be the length and width of the rectangle Then area of rectangle is

Q: A company making luggages have these requirements to follow. The length is 15 inches greater than…

A: According to question,Length is 15 inches greater than depth and the sum of length, width and depth…

Q: An expecting mother wants to convert a corner of the nursery in her house into a rectangular playpen…

A: Let x and y be the dimension of the rectangular playpen. Given

Q: Find two numbers whose sum is 40 and whose product is a maximum.

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Q: Find the maximum number of goldfish you can put in a cylindrical tank whose diameter is 8 meters and…

A: Fish would be put in the tank, that is, the volume of the tank. Hence the volume of the tank helps…

Q: A rectangular garden is 5 ft longer than it is wide. Its area is 6000 ft². What are its dimensions?…

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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: Mang Toti has a rectangular lot with one side against the wall. If he has 160m of fencing materials,…

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Q: The top of a box is a rectangle with a perimeter of 72 inches. If the box is 8 inches high, what…

A: Given:The box (or cuboid) has the height 8 inches(i.e. h = 8 in.) and the perimeter of the top of…

Q: A farmer wants to fence a rectangular field and then divide it in half with a fence down the middle…

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Q: A rectangular garden has a width smaller than twice the length of 10 feet. Find the dimensions if it…

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Q: Three pens of the same size are to be built along an existing fence. If 480 feet of fencing is…

A:

Q: Find the dimensions of the rectangular box of maximum volume if the sum of the length, width, and…

A: To find dimension of the rectangular box of maximum volume  Given sum of length, width and height…

Q: A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the…

A:

Q: The length of a rectangle exceeds it's width by 8 cm and the area of the rectangle is 240 sq.cm.Find…

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Q: What positive number exceeds its cube by the maximum amount?

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Q: A 20 feet wire is cut into two pieces. To form an isosceles triangle and a circle, find the…

A: Concept: If a solid is formed through a wire then the perimeter of the solid is equal to the length…

Q: The perimeter of a rectangle is to be no greater than 80 centimeters and the width must be 10…

A: let length be x and width is given to be 10. Perimeter of a rectangle is defined as 2(length +…

Q: Find two numbers whose sum is 20 and whose product is a maximum

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Q: A rectangle has a perimeter of 40m. What could be the maximum area of the rectangle?

A: A rectangle has a perimeter of 40 m. Let x and y be the length and width of the rectangle. Now…

Q: One side of a triangle is three times as long as another side, and the third side is 12 inches long.…

A: Let the length of the shortest side of triangle be x inches. given that One side of a triangle is…

Q: . The front face of a tent is triangular and the height of the triangle is two-thirds of the base.…

A: Consider the given:  The objective is the find the dimensions of the tent:  Base = xHeight =…

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: The maximum area of a rectangle whose perimeter is 144cm is ... cm^2

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Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

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Q: Find two numbers whose sum is a, if the product of one by the cube of the other is to be a maximum.

A: According to our guidelines In case of multiple questions we are supposed to answer the first…

Q: A rectangular dog pen is constructed using a barn wall as one side 66 meters  of fencing for the…

A: NOTE: Refresh your page if you can't see any equations. . x=width of the rectangle y=length of the…

Q: A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the…

A: Let the length and width of the rectangular garden be x and y respectively fence…

Q: A farmer wants to create four rectangular corral's to separate his livestock. He has 750m of fencing…

A: Let the dimension of the each rectangular corral be, x m by y m.The perimeter of one rectangular…

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: Both these questions can be solved by applying the concept of maxima and minima.

Q: The perimeter of a rectangle is to be no less than 72 centimeters and the width must be 17…

A: In the question we have to find minimum length of the rectangle.

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

A:

Q: Find the dimensions of a rectangle with a perimeter of 200 feet that has the maximum area.

A: Given that the perimeter of the rectangle is 200 feet.   Suppose that the length of the rectangle x…

Q: The Perimeter of a rectangle is 20 feet. Of all possible dimensions, the maximum area is 25 square…

A: Let the length = x Width= y So, perimeter= 2(x+y)=20  x+y=10 y=10-x

Q: The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than…

A: Let the shortest side= x cm  so the longest side= 3x cm  third side= 3x-2 cm

Q: A 20 feet wire is cut into two pieces. To form an isosceles triangle and a circle, find the…

A:

Q: What is the maximum area that can be completed with 240 feet of fencing? What are the dimensions?

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Q: A farmer has 20 feet of fencing, and he wishes to make from it a rectangular pen for his pig Wilbur,…

A: Let, width= x, length = y So, total fence needed= 2x+y=20 feet  y= 20-2x

Q: The perimeter of a rectangle is to be no greater than 100 centimeters and the width must be 15…

A: Perimeter of rectangle = 2 ( length + width)  Given width = 15 cm  and  perimeter of a rectangle…

Q: Four feet of wire is to be used to form a square and a circle. How much of the wire should be used…

A: We have given the length of a wire 4 ft that is used to make square and circle;

Q: A piece of wire, 100 cm long, needs to be bent to form a rectangle. Determine the dimensions of a…

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Q: Find the length and width of a rectangle that has 80 meters perimeter and a maximum area.

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Q: A farmer decides to enclose a rectangular​ garden, using the side of a barn as one side of the…

A:

Q: Find two numbers whose sum is 50 and whose product is a maximum.

A: To find two numbers whose sum is 50 and whose product is a maximum.

Q: The front face of a tent is triangular and the height of the triangle is two-thirds of the base. The…

A:

Q: The base of a triangle measures 40 inches minus twice the measure of its height. For what measure of…

A: Let h is the height of the triangle Then, according to question  base=40-2h Then…

Q: A rancher has 1500 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will…

A: Refer to the questionLet the common sides of two rectangular corrals be x then the sketch for the…