A rectangle is inscribed in a right triangle of sides 5, 12, and 13. What are the dimensions of the rectangle of greatest area if the it's sides coincides with the legs of the triangle

Q: If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the…

A: Let dimesnion of the region is x and ysince, the farmer has 162 feet of fencingtherefore,…

Q: Find the dimensions of the largest rectangle that can be inscribed in an isosceles triangle if one…

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Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The…

A: Here we have to find the length and width of the rectangle that has perimeter of 32 with maximum…

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

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Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Consider x to be the length and y to be the width of the rectangular region as shown below.

Q: Show that of all the rectangles with a given perimeter,the one with greatest area is a square.

A: Let the perimeter P is given.  Let, length = x and width= y So, 2(x+y)=P Or, x+y=P/2 Or, y= (P/2) -…

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: A rectangle has a base of 16 inches and an altitude of 8 inches. Find the dimension of the largest…

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Q: When a carton of apples were packed into bags of 4, there would be 3 apples left over. When the same…

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Q: Fill a 4X4 magic square with real numbers so that the product of the numbers in each row is less…

A: For finding the required answer first construct the magic square with order 4.…

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 rectangle is inscribed in a right triangle. If the triangle has sides of length 5, 12, and 13,…

A: Let x and y be the length and breadth of the rectangle inscribed in the triangle. Let us take the…

Q: Find the dimensions of the largest rectangle that can be inscribed in the right triangle with side…

A: Area of rectangle= length×bredth

Q: Show that among all rectangles with a given perimeter, the square is the one with the maximum area.

A: A rectangle is a quadrilateral whose opposite sides are equal and parallel to each other. The…

Q: A triangle has a base of 16 inches and an altitude of 8 inches. Find the dimensions of the largest…

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Q: Find four consecutive odd internet’s such that four times the sun of the first and third is four…

A: To find four consecutive odd integers such that four times the sum of the first and third is four…

Q: Find the dimensions of a closed 800 m3 cylindrical oil storage tank that can be made from the least…

A: Given, The volume of cylindrical  oil storage tank  = 800 m3   We have to find the dimensions of…

Q: Find the rectangle whose vertex is haveng on possible max comum area

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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: Find the dimensions of the largest field that can be enclosed with this amount of fencing, and find…

A: The total length of fence is 148ft.

Q: 2) The length of a rectangle exceeds the width by 10 cm. If each dimension were increased by 3 cm,…

A: Given that length of rectangle exceed width by 10 cm. Area of rectangle after 3 cm increase in each…

Q: Suppose you must use 1x“-tile and 10 x-tiles. You only have up to 15 1-til use. How many of the…

A: Introduction: A rectangle is a quadrilateral with equal angles and opposite sides that are equal and…

Q: Find the maximal area of a right triangle with hypotenuse of length 7.

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Q: Of all rectangles with a perimeter of 28​,which one has the maximum​ area? (Give the​ dimensions.)

A: We can find the dimensions as below.

Q: Find the maximal area of a right triangle with hypotenuse of length 3.

A: Please refer the attached image for complete solution.

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: Find the dimensions of rectangle with perimeter 92 m whose area is as large as possible

A: We have given rectangle of perimeter is 92m. Let the length and breadth of the rectangle are x and…

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 maximal area of a right triangle with hypotenuse of length 5.

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

Q: Among all rectangles that have Perimeter of 627+, find the dimensions of the one with largest area?

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Q: Of all rectangle that have a perimeter of 42 feet, find the dimensions of the one with the largest…

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Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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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: 2. Show that of all rectangles with diagonal of length c, the square has the largest area.

A: All rectangles with diagonal of length c, the square has the largest area.

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

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Q: An open-topped box can be created by cutting congruent squares from each of the four corners of a…

A: Given, l= 30-2x b= 20-2x h= x Volume= 1008 cm³

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: A farmer wants to fence in an area of 200 square feet in a rectangular field and then divide it in…

A: Given Area of rectangular field =200 square feet

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: A one-story building having a rectangular floor space of 13200 ft2 is to be constructed where a 22ft…

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Q: Prove that the sum of the squares of three consecutive integers cannotbe a square.

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

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Q: Suppose two squares of the same color are removed from an 8 x 8 chessboard. Is it possible to tile…

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Q: A batch of cookies can be divided into equal shares among 2, 3, 4, 5 and 6 people with no cookies…

A: Given that, The batch of cookies can be divided into equal shares among 2,3,4,5 and 6 people with no…

Q: A rectangle is inscribed in a right triangle of sides 5, 12, and 13. What are the dimensions of the…

A: Let x and y  be the side lengths of  the rectangle then area is A=xy And by similar triangles are,…

Q: The base of a three-dimensional figure is bound by the semi-circle y = √9-x². Vertical cross…

A: Given: Let us consider the given semi-circle, y=9-x2 Let's determine the Area of the square.

Q: Find the maximal area of a right triangle with hypotenuse of length 6. 5.59

A: Solving the problem by finding the maximal area of triangle.

Q: The technique of boxing in a triangle and determing its area by using rectangle and right triangle…

A: Let ABC is triangle with vertices, Ax1,y1,Bx2,y2,Cx3,y3. WhereDx1,0, Ex2,0, Fx3,0 are points on…

Q: Show that a 6 × n board (n ≥ 2) can be tiled with L-shaped tiles, without gap and overlapping. Each…

A: Before we begin proving the statement, we shall understand the shapes. An L-shaped three-square tile…

Q: 2. A rectangular lot adjacent to a highway is to be enclosed by a fence. If the fencing costs P250…

A: The rectangular plot has length x  and width y cost of the fence is 250(length along highway )…