An isosceles triangle has base 6 and height 15. Find the maximum possible area of a rectangle that can be placed inside the triangle with one side on the base of the triangle. (Hint: Similar triangles may be of assistance.) Areamax =

Q: 15. A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from…

A:

Q: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

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

A: According to given question we have where AB = 14 , BC = 12EF =BD = x and FD=EB = yArea of the…

Q: A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the…

A:

Q: If an isosceles triangle has a fixed perimeter P, find the dimensions that maximize the area. Your…

A: Given: An isosceles triangle is given with perimeter P. The objective is to find the dimensions of…

Q: The legs of a right triangle have lengths 3 cm and 4 cm, respectively. A rectangle is inscribed in…

A: This question can be solved using the concept of maxima and minima.

Q: An isosceles triangle has base 7 and height 12. Find the maximum possible area of a rectangle that…

A: Refer to the question. Sketch the isosceles triangle having base 7 and height 12 and a rectangle…

Q: A window on a new house is designed as a rectangle with a semicircle on the top. If the window is…

A:

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 2500 yd…

A:

Q: A rectangle has a fixed perimeter of 12. Find the dimensions of the rectangle so that its area is…

A: Let's find.

Q: a. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Note: According to Bartleby guidelines; For more than one question asked only the first one is to be…

Q: Given a rectangular garden with perimeter of 31.20m, determine the maximum possible area, AND the…

A:

Q: A farmer has a 200 m fencing material to enclose two adjacent sides rectangular field. What…

A: We use second derivative test to find out dimensions where area is maximum

Q: A piece of sheet metal is rectangular, 5 feet wide and 8 feet long. Congruent squares are to be cut…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 8. Find the dimensions of the rectangular box, open at the top, which has a maximum volume if…

A: Given surface area is 18 square feet.

Q: 15. A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from…

A: To find: The size of square to be cut of each corner to get a box with maximum volume. Given: The…

Q: A farmer wants to build a riding arena in the shape of a rectangle topped by two semicircles. Find…

A: If you like the solution then please give it a thumbs up.. The Answer is:      Maximum Area = 160652…

Q: Of all rectangles with a fixed perimeter of P, which one has the maximum area? (Give the dimensions…

A: let the length of rectangle is l and width is bthen perimeter (P)=2(l+b)sol+b=P2or l=P2-b

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. Find the dimensions of a…

A: Given that the perimeter is fixed.Let us assume that the length of the rectangle part which is also…

Q: Answer it correctly, neatly, and comprehensively.  Written answer only.  A rectangular box with…

A:

Q: A triangular lot, where all its three sides have the same length, is to contain a triangular…

A: The figure is shown below: △ABC represents triangular lot.△DEF represents traingular building

Q: 8. A rectangular dog pen is being built against the side of a house using 96 ft of fencing for the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: e) A farmer wishes to enclose three pens with fencing, as shown. If the farmer has 700 feet of…

A: 700 feet of fencing to work .

Q: b) Find the maximum volume that such a box can have.

A:

Q: A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. II the…

A: The given a pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the…

Q: An open box (no top) is to be made by cutting congruent squares from each corner of a 12-inch by…

A:

Q: 2. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible? Find…

A: Here we have to find the dimensions of w rectangle with perimeter 100m whose area is as large as…

Q: A Norman window is constructed by adjoining a semicircle to the top of a rectangular window, as…

A:

Q: A rectangular box has a square base. If the sum of the height and the perimeter of the square base…

A: Explanation of the answer is as follows

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A:

Q: A window is being built with the lower part being a rectangle and the top part being a semicircle…

A: Window shape- A rectangle with dimension (h×2r) and a semi circle with radius r. Framing material…

Q: An isosceles triangle has base 9 and height 11. Find the maximum possible area of a rectangle that…

A:

Q: 8. A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: A rectangular figure is given. Let, the length of parallel side of division be y and the length of…

Q: An isosceles triangle has base 7 and height 12. Find the maximum possible area of a rectangle that…

A: For maximum area dA/dt=0.

Q: A farmer has 800 feet of fencing with which to build a holding pin with a cattle shoot at one end as…

A:

Q: A rectangular tank with a square base, an open top, and a volume of 8788 ft 3 is to be constructed…

A: A rectangular tank has square base Let x be the base of the tank  and y be the height  x is the…

Q: 0. Find the dimensions of a rectangle of maximum area that can be inscribed in a circle of radius 4…

A: Given:     radius ( r ) = 4 cm

Q: 1. Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle…

A: From the given problem:   Perimeter=P=1000 m   Let the length of the rectangle 'abcd' is 'X' and…

Q: Suppose that a family wants to fence in an area of their yard for a vegetable garden to keep out…

A:

Q: An isosceles triangle has a perimeter of 30cm. What is the length of the base if its area is to be…

A:

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake​ Beach, using 1400…

A: Given,          A lifeguard needs to rope off a rectangular swimming area in front of Long Lake…

Q: A rectangular box without a lid is to be made from 12 m2 of cardboard. Find the maximum volume of…

A: Given that a rectangular box without a lid is to be made from 12 m² of cardboard.

Q: square corners are cut out so that the sides can be folded up to make a box. What dimensions will…

A:

Q: .A Norman window has the outline of a semicircle on top of a rectangle, as shown in the figure.…

A:

Q: a) A triangle is inscribed in a semi-circle, its hypotenuse lies on the diameter of the semi-circle.…

A: Given: Let ∆ABC is inscribed in semicircle. The angle inscribed in a semicircle is always a right…

Q: The perimeter of a triangle is 102cm and its area is 431.1554cm2. Find the maximum diameter of a…

A: Given: Area of triangle = 431.1554 cm2 Perimeter of triangle = 102 cm We know that the incircle of a…

Q: Please help. Thank you!

A: According to the given information, a pentagon is formed by adding two sides of same length to…

Q: A farmer wishes to enclose a rectangular region bordering a barn with fencing, as shown in the…

A: Assume the below figure top be the given figure as mentioned in the question. Let the length of the…