The sum of the base and the height of a triangle is 30 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of cm and a base of cm.

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 dimensions of a rectangle with an area of 2568 m^2 whose perimeter is as small as possible.

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Q: Find the dimensions of a rectangle with area is 120 m² whose perimeter is as small as possible

A: topic - application of derivatives

Q: The width of a rectangular lawn is 12 meters less than the length. Find the dimensions of the lawn…

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Q: The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the…

A: I use second derivative test to find out dimensions where area is minimum

Q: Find the dimensions of a rectangle whose width is 7 meters less than its length, and whose area is…

A: Answer:  the dimension of rectangle : length and width are as follows :

Q: A rectangular playing field lies in the interior of an elliptical track that is 40 yards wide and…

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Q: The length of the rectangular swimming pool in Jake’s yard is 2ft more than twice its width. Find…

A: The length of the rectangular swimming pool in Jake’s yard is 2ft more than twice its width. Now let…

Q: The breadth of a room is twice its height , one half of its length and the volume of the room is 512…

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

A: Given that, the perimeter of the rectangle is 100m.  Let, the length be l and the breadth be b.  So,…

Q: The area of a rectangle is 45 m sqaured, and the length of the rectangle is 1 m more than twice the…

A: The area of a rectangle is 45 m square, and the length of the rectangle is 1 m more than twice the…

Q: The Length of a new rectangular playing field is 2 yards longer than triple the width. If the…

A: Let the rectangle with is x yards .Since , the length of rectangleis 24 yards longer than tripple…

Q: The area of a rectangle is 21 yd", and the length of the rectangle is 1 yd less than twice the…

A: Area of the Rectangle, A = 21 yd2 Length of the Rectangle, l = ? Width of the Rectangle, w = ?

Q: The prism has a dimension of (x+1) meters, (x+5) meters and (x+3) meters respectively. If the volume…

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Q: The measures of the sides of the square base of a box are twice the measure of the height of the…

A: given: the measures of the sides of the square base of a box are twice the measure of the height of…

Q: The volume of a swimming pool is 2x^3+5x^2-28x-15.If the height of the pool is (x-3) meters,what are…

A: We are given :Volume of a swimming pool V(x)=2x3+5x2-28x-15 Now Length be l(x) ,breadth be b(x) and…

Q: Find the length and the width of a rectangle that has perimeter 80 cm and a maximumarea

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

A: We need to find dimensions of trapezoid.

Q: Find the dimensions of a rectangle with are is 625 m^(2) whose perimeter is as small as possible.

A: Let x=Length and y=Width of rectangle. From the question, Area of rectangle is 625 m2 Area=xy=625…

Q: The length of a rectangle is 2 m longer than its width and the area of the rectangle is 400 m2. Find…

A: let the width is b meter  then length is (b+2) meter

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: 4) The sum of the bases and altitude of an isosceles trapezoid is 36cm. find the altitude if the…

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Q: A garden is to be laid out in a rectangular area and protected by a wire fence. What is the largest…

A: Given: We have to find the largest possible area of the rectangular garden, 100 running feet of the…

Q: The and bottom margins of a poster are 6 cm and the side margins are each 8 cm. If the area of…

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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: The sugarcane plantation below has an area of (x 2 + 5x + 6) hm^2 . What are its possible…

A: Given:- The sugarcane plantation below has an area of (x 2 + 5x + 6) hm^2 . To find:- Possible…

Q: The area of a rectangle is  77 ft2 , and the length of the rectangle is  10 ft  less than three…

A: Let l be the length and w be the width of the rectangle. Then according to given data, we have

Q: The length of the first side of a triangle is twice the length of the second side, and the length of…

A: We know that perimeter of triangle is , P = a + b + c  Here a , b and c are the sides of triangle .

Q: A rectangle is 7 cm longer than it is wide. Find the dimensions of the rectangle if its area is 337…

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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: You have 272 feet of fencing and would like to build a playpen for your two show poodles.  The…

A: We use second derivative test to find largest area dimensions for each poodles

Q: The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 33 m.…

A: CONCEPT:- If length of a rectangle is 'l' and width is 'b' then area of rectangle (A) is given…

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

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Q: The length of a rectangle is 8cm less than twice width. If the area of the rectangle is 42cm2. Find…

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Q: Find the length and width of a rectangle that has perimeter 48 meters and maximumarea.

A: Let l and b are the length and width of a rectangle.Perimeter of the rectangle is 48 meters.That is,…

Q: The side of a square exceeds the side of the another squares by 4 cm and the sum of the areas of two…

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Q: The length of a rectangle is three times its width.If the perimeter of the rectangle is 80 m find…

A: Consider the provided question,Let the width of a rectangle  = x mSo, the length of the rectangle =…

Q: A rectangle has a length 6 more than its width. If the perimeter of the rectangle is 40 m, what are…

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Q: The area of a rectangle is 28 m² and the length of the rectangle is 5 m less than three times the…

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Q: the length of a rectangle is 13centimeters less then six times its width its area is 28square…

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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 perimeter 40 whose area is as large as possible. What is the…

A: Consider the rectangle with length x and width y, then 2x+2y=40x+y=20y=20-x...1 Here, the objective…

Q: A backyard pool has a concrete walkway around it that is 5 feet wide on all sides.The total area of…

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Q: A farmer has 2, 000 feet of fence and wishes to build two identical rectangular enclosures, as in…

A: Given query is to find the dimensions of the sides to maximize the area.

Q: The length of a rectangle is four times its width.If the perimeter of the rectangle is  80 in, find…

A: Let the width = x in  So the length = 4x in

Q: The volume of the swimming pool is given by 3x3 + 4x? - 17x - 6. If the height of the pool is given…

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Q: Find the dimensions of the rectangle in the figure shown below that will give the maximum area, if…

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

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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…