An expecting mother wants to convert a corner of the nursery in her house into a rectangular playpen by enclosing the corner of the room with two fences. If the woman has 10 feet of fencing material, what is the maximum area the playpen could encompass?

Q: A cable that has 50 cm is divided into two parts. One part is used to make an equilateral triangle…

A: Length of cable = 50 cm

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 standard elevator in a midrise building can hold a maximum weight of about 3 2/3 tons. Assuming an…

A: We first convert tons into pounds

Q: A closed box, whose length is twice its width, is to have a surface area of 192 sq. inches. Find the…

A: It's a closed box, so it has a top Let ? be the width of the box. Then its length is 2?. And the top…

Q: A delivery company wants to come up with a package box that has a square base and a volume of 40…

A: Given, Let's assume the side of the square base = a Height of the box  = h Volume = area of  base *…

Q: A farmer buys 120 m of fence. He wants to make 2 cages of 4 rectangles with the same length for his…

A: Let x and y be the  length and width of cage respectively (equals to dimensions of rectangle) total…

Q: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

A: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

Q: Jim wants to build a rectangular parking lot along a busy street but only has 2,800 feet of fencing…

A: This question is related to application of derivative.

Q: A rancher wants to fence in an area of 500,000 square feet in a rectangular field and then divide it…

A: Consider a rectangular field of length l and width b as shown in the figure and than use the…

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

A:

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: The sum of the sides of an isosceles triangle is 24ft. find the lengths of the sides that maximize…

A: Given:              Let ΔABC be an isosceles triangle with AB=AC.Let AD be the altitude of the…

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

A:

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

A:

Q: An open box is to be made from a 6 ft by 16 ft reetangulas card board by cutting out equaL squares…

A:

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…

A:

Q: Helen has 28 m of fencing which she can use to surrounda pen for her pigs. What is the maximum area…

A:

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

A:

Q: A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it…

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: An animal shelter has 160 feet of fencing to enclose two adjacent rectangular playpenareas for dogs.…

A: Sketch the adjacent rectangular playpen areas for dogs as shown below.

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

A:

Q: A rancher wants to fence in an area of 1,500,000 square feet in a rectangular field and then divide…

A: Let one side of area = x, other side = yLet extra fencing be parallel to sides of length y.So we…

Q: A piece of wire, L inches long is to be used to form a square and a circle. How much of the wire…

A: A piece of wire is used to form a square in first case and then a circle.

Q: A rancher wants to fence in an area of 1,000,000 square feet in a rectangular field and then divide…

A: Let, x and y be the dimension of the rectangle. So, xy=1000000⇒y=1000000x...(1) Now, the fence…

Q: Ricardo wants to cover this 5'' by 10'' by 8'' box with wrapping paper. What is the minimum number…

A: Given that Ricardo wants to cover this 5'' by 10'' by 8'' box with wrapping paper.

Q: Glenview Community College wants to construct a rectangular parking lot on land bordered on one side…

A: Given : Let x be the width of the lot, and 380-2x be the length.  The area of the rectangular is…

Q: A rectangular rice field is to be fenced along 4 sides and, in the middle, to divide it into two…

A:

Q: You have 40 feet of fence to enclose a rectangular garden with two subdivisions. What is the maximum…

A:

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: Mr. Raymundo has enough materials to fence 90 meters. What are the dimensions of the rectangular lot…

A: Let the length and width of the rectangle be x and y. Then the perimeter of the rectangle is = 2x+y…

Q: A 10-ft wire is to be formed into an equilateral triangle and a square. What is the measure of the…

A: Given;+ A 10-ft wire is to be formed into an equilateral triangle and a square. To find What is the…

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: Jim wants to build a rectangular parking lot along a busy street but only has 2,100 feet of fencing…

A:

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

A:

Q: When enclosing 3 sides, the maximum area for a given rectangular area is obtained by forming a…

A: Given:Length is twice the ?

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

A:

Q: A rancher wants to fence in an area of 2,000,000 square feet in a rectangular field and then divide…

A: see below the answer and calculation

Q: A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it…

A: Here Area A=500000 square feet where, Area=LLenght×wwidth

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

A:

Q: A farmer has 1,200 feet of fence and wishes to build two identical rectangular enclosures, as in the…

A:

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

A:

Q: A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide…

A:

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…