Prove analytically that the lengths of the diagonals of a rectangle are equal.

Q: Prove ABCD is a parallelogram. Justify mathematically and explain.

A: Given vertices of quadrilateral are A(-1,3) B(3,2) C(2,-5) D(-2,-4) Prove ABCD is a parallelogram

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: All parallelogram are squares  •True  •False

A: To Determine:  Is the statement is True or False All parallelogram are squares

Q: Can 2 diagonals in cube ever be mapped on to a single diagonal?  No, why?

A:

Q: Without using a computer or a calculator, estimate the change in length of a space diagonal of a box…

A: Solution -  We have been given dimensions of two boxes.  And the difference between their space…

Q: A ladybug crawls around the outside of a rectangle that measures 9.5 cm by 7.5 cm. The ladybug stays…

A: The dimensions of rectangle 9.5 cm by 7.5 cm The ladybug stay 3.2 cm from the rectangle at all time…

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

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Q: find its dimensions of height and length of ba:

A:

Q: Which of the following would show that the diagonals of quadrilateral JKLM on the coordinate plane…

A: The given triangle JKLM is,

Q: Show that the rectangle which has maximum area for a given perimeter is a square.

A: This problem can be solved by expressing the area of the rectangle as a function of single variable…

Q: Find the angle between the diagonal of a cube and one of its edges.

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: Prove that the diagonals of a rectangle are equal.

A: Let assume PQRS is the rectangle with                              PR and…

Q: Prove that the sum ofthe squares of the sides of a rhombus s equal to the sum of the squares of its…

A:

Q: What is the sum of the coordinates at which the diagonals of ABCD intersect?

A: From the given figure, The equation of the diagonals can be written as :

Q: A cube has four diagonals. Show that no two of them are perpendicular.

A: Given: A cube has four diagonals.

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: Prove that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum…

A: Let the sides of the parallelogram be 'l' with longest and 'b' with shortest parallel lines and…

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: Prove analytically that the sum of the squares of the four sides of a parallelogram is equal to the…

A: Apollonius's theorem   for triangle ABC with M being the midpoint of BC, the following equation…

Q: Suppose that the width of certain rectangular is three centimeters less than two times its length.…

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: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given  Total length of the fence=2500 m Letl=length of the plotb=width of the plot

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: 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 analytically that if the diagonals of a parallelogram rectangle. are equal, then the…

A: Given:-  Diagonals of parallelogram are equal.To proof  Parallelogram is a Rectangle.

Q: Suppose AT bisects 2CAR. If mzCAT = 5x and M2CAR = 9x +7, what is mzTAR? %3D %3D

A: Given that AT bisect ∠CAR if m∠CAT = 5x and m∠CAR=9x+7To find :m∠TAR Solution…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given length of wire is 700 m. rectangular plot's three sides are bounded by electric fence.

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: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius 10. *

A: From the given figure we can derive length and breadth. below are the steps.

Q: A ladybug crawls around the outside of a rectangle that measures 9.5 cm by 6.5 cm. The ladybug stays…

A:

Q: Prove that the diagonals of a trapezoid divide themselves proportionally.

A:

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: 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: Prove that the quadrilateral with vertices A(0,0), B(4,3), C(7,-1) and D(3,-4) is a square.

A: →In a quadrilateral, if all sides are equal then quadrilateral is a square. →Calculate the length of…

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: help!! the assignment is on quadrilaterals, similar triangles, and circles! I really need this…

A:

Q: Prove that if ABCD is a parallelogram, then its diagonals bisect each other.

A: Let us consider a paralellogram ABCD which have diagonals AC And BD and intersect at point E

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Let a and b be the sides of a retangular fence.

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

A:

Q: If the diagonals of a rectangle are perpendicular, then the rectangle is a square.

A: Consider the given information as, If the diagonal of a rectangle are perpendicular, then the…

Q: Show that squares are the only rect-angles with perpendicular diagonals.

A: Consider u and v as the sides of the rectangle.The diagonals are perpendicular.Consider the…

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:

Q: Prove that the diagonals of a rhombus (parallelogram with 4 equal sides) are perpendicular to each…

A: A parallelogram is a rhombus if all sides are equal.

Q: If a side of a square has length 5 cm, then a diagonal of the square haslength _______ cm.

A: Here given a side of a square has length 5 cm