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

Q: The prism is bisected by the xz-plane. If P = (5, 2, 4), what is the area of the rectangle formed by…

A:

Q: 34. Prove by the indirect method: "The length of a diagonal of a square is not equal in length to…

A: Prove by contradiction

Q: Show that among all rectangles with an 8-m perimeter, the one with largest area is a square.

A: Let l be the length and b be the breadth of the rectangle.

Q: What is the area of the triangle formed if it bounded by the x and y axes and the line,  2x - 3y =9?

A: Here we have to find the area of the traingle since Area of  Triangle = 1/2 *(hight)*base

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: Prove that of all rectangles with given perimeter, the square has the greatest area.

A:

Q: Prove that the area of a circle circumscribed about a square is twice the area of the circle…

A: Prove that the area of a circle circumscribed about a square is twice the area of the circle…

Q: Find the area of a quadrilateral with vertices A( - 1 . - 1), 5(9, 4), C(20, 6).and D(10, 1).

A:

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in the right…

A: Given: AF=4, AD=5, and DF=3. AC= (4-h) and DE= (3-w) Therefore,

Q: Show that all the rectangles with a given perimeter , the square has the largest area

A:

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

A: using second derivative test to find if square has largest area.

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: Find the area of the largest rectangle that can be inscribed in an equilateral triangle of side…

A: Given: A rectangle inscribed in an equilateral triangle of side L assuming one side of the rectangle…

Q: 5. Find the length of the shorter diagonal in a rhombus with an area of 30 m² if the lengths of the…

A: Given: Area =30m2 length of diagonal differ by 4

Q: Find the area of an octagon if the distance from center to vertex is 25 in.

A: The area of regular octagon with circumradius r(distance from center to vertex ): A = 22r2

Q: J (1,4) M(-1, 2) К(3,2) L (1, – 3)

A:

Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0, 0), Q(3, 4, 0), R(0,…

A: Let, P, Q, R, S be the four vertices of a parallelepiped. Then, we find the vectors, a=PQb=PRc=PS…

Q: Find the area of a square with diagonals of length d

A: Given: Length of diagonal = d To Find: Area of square

Q: A rectangle has base length x + 3, altitude length x + 1, and diagonals of length 2x each. What are…

A: The base, altitude and diagonal of a rectangle make a right triangle.

Q: What type of polygon must have a diagonal such that at least part of the diagonal falls in the…

A: It is known that, a quadrilateral is a plane figure that is made up of four line segments closing in…

Q: Find the volume of a parallelepiped if four of its eight vertices are A(0, 0, 0), B(1, 2, 0), C(0,…

A: Draw the diagram roughly

Q: Prove by the indirect method: “The length of a diagonal of a square is not equal in length to the…

A: Introduction: There are some basic methods that are used to prove any mathematical statement. These…

Q: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r

A: Let the length of the rectangle be 2x and the width of the rectangle be y. From the figure, the…

Q: Find the length of the longer diagonal in a rhombus with sides of length 12 and a smaller diagonal…

A:

Q: A rectangle with sides measuring x in. and 4x-1 in. has an area of 663in.^2. What are the dimensions…

A:

Q: 2 Find the volume of the parallelepiped whose edges are represented by A =î - 13ĵ+ 4k, B = 3î +2j-7k…

A:

Q: Find the length of a diagonal of a square with perimeter 16

A: Let the side length of the square is a, Then the perimeter of a square is given as, P=4aa=P4=164=4…

Q: Find the area of the parallelogram that has u = (1, 3, 0) and v = (−1, 0, 2) as adjacent sides.

A: Now cross product is,

Q: Prove that ABCD is a square if A(1,3), B(2,0), C(5,1) and D(4,4).

A: Consider the graph shown below:

Q: Prove that a parallelogram is a rectangle if and only if its diagonals are equal in length. (This…

A: Let ABCD be a parallelogram. Given AC and BD are diagonals of parallelogram in equal length. In…

Q: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral…

A:

Q: Theorem. The diagonals of a rectangle bisect each other and have the same length.

A:

Q: Prove that a parallelo-gram is a rectangle if and only if its diagonals are equal in length. (This…

A: Consider a parallelogram ABCD having diagonals AC and BD such that, AC=BD.

Q: Prove that ABCD is a square

A: If ABCD  is a square then length of all the sides will be equal, That means. AB=BC=CD=DA.  To find…

Q: Of all rectangles with area 400 in2, what are the dimensions of the one with the minimum perimeter?…

A:

Q: Prove that among all rectangles with area 100 square units,the square has the smallest perimeter.

A: The area of the rectangle is defined as the product of length and breadth of the rectangle, whereas…

Q: Find the area of a square whose diagonal has length 14.5 cm.

A: The diagonal length of the square is 14.5 cm. we have to find its area.

Q: How many diagonals can be drawn from a dodecagon?

A:

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in the right…

A: Given the figure:

Q: Prove that the area of a square whose diagonal has length d is A = ¿d?.

A: The length of the diagonal of a square is d. Now let a be the length of the side of a square. Now…

Q: Find the area of the largest rectangle that fits into the triangle with sides х — %3D1 ахis, у —…

A:

Q: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of…

A: Area of semi circle having diameter of a is, Aa=πa222Aa=πa28         ...(1)  Area of semi circle…

Q: Prove analytically that the perpendicular bisector of the sides of a triangle are concurrent.

A:

Q: Find the area of a square whose diagonal has length V10 in.

A:

Q: Find the area (in cm^2) of the largest rectangle that can be inscribed in a right triangle with legs…

A:

Q: 2. Among all rectangles that have perimeter of (54+0) ft, find the dimensions of the one with…

A:

Q: Find the length of the diagonal of a cube whose total surface area is 15 sq.cm

A: To find the length of diagonal if a cube whose total surface area is 15 sq cm

Q: Prove the area of a rhombus is one-half the product of the lengths of the diagonals.

A: To prove the area formula for a Rhombus

Q: Determine the dimensions of the largest rectangle that could be inscribed in a semi-circle of radius…

A: