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What is the sum of the lengths of the diagonals within a rhombus that has a perimeter of 78 cm and an area of 270 square cm showing how answer is worked out?
The rhombus will consist of 4 right angle triangles each having an hypotenuse of 19.5 cm and an area of 67.5 square cm
Square 19.5 and square (2*67.5) then find two numbers each of which have been squared that have a sum of 380.25 and a product of 18225
Let the numbers be x and y:-
If: x+y = 380.25
Then: y = 380.25-x
If xy = 18225
Then: x(380.25-x) = 18225
So: 380.25x -x^2 -18225 = 0
Solving the above quadratic equation: x = 324 or x = 56.25 meaning y = 56.25
Square root of 324 = 18 and square root of 56.25 = 7.5 which are sides of triangles
Therefore sum of diagonals: 36+15 = 51 cm
Check: 0.5*36*15 = 270 square cm
Check: 18^2 + 7.5^2 = 380.25 and its square root is 19.5
Check: 4*19.5 = 78 cm which is the perimeter
What else can I help you with?
What is the area and perimeter of a rhombus whose diagonals are in lengths of 7.5 cm and 10 cm showing work?
Area of the rhombus: 0.5*7.5*10 = 37.5 square cm Perimeter using Pythagoras: 4*square root of (3.75^2 plus 5^2) = 25 cm
What is the perimeter of a rhombus whose diagonals add up to 42.5 cm and has an area of 187.5 square cm showing work?
Double the area and find 2 numbers that have a sum of 42.5 and a product of 375 which will work out as 30 and 12.5 by using the quadratic equation formula. Therefore the diagonals are of lengths 30 and 12.5 which will intersect each other half way at right angles forming 4 right angle triangles inside the rhombus with sides of 15 cm and 6.25 cm Using Pythagoras' theorem each out side length of the rhombus is 16.25 cm and so 4 times 16.25 = 65 cm which is the perimeter of the rhombus.
What is the perimeter of a rhombus whose diagonals add up to 24.5 cm and has an area of 73.5 square cm showing all work?
Let the diagonals be x and yIf: x+y = 24.5 then y = 24.5-xIf: 0.5xy = 73.5 then 0.5x(24.5-x) = 73.5So: 24.5x -x^2 -147 = 0Solving the above quadratic equation: x = 14 or 10.5The rhombus will consist of 4 right angles of base 5.25 and height 7Using Pythagoras' theorem each side of the rhombus is 8.75 cmTherefore its perimeter is: 4*8.75 = 35 cm
What is the area of a rhombus when one of its diagonals is 11.8 cm in length and has a perimeter of 29 cm showing work and answer?
Perimeter = 29 cm so each side is 7.25 cm. The triangle formed by the diagonal and two sides has sides of 7.25, 7.25 and 11.8 cm so, using Heron's formula, its area is 24.9 square cm. Therefore, the area of the rhombus is twice that = 49.7 square cm.
What is the perimeter of a rhombus when one of its diagonals is greater than the other diagonal by 5 cm with an area of 150 square cm showing key aspects of work?
Let the diagonals be x+5 and x:- If: 0.5*(x+5)*x = 150 sq cm Then: x2+5x-300 = 0 Solving the above by means of the quadratic equation formula: x = +15 Therefore: diagonals are 15 cm and 20 cm The rhombus has 4 interior right angle triangles each having an hypotenuse Dimensions of their sides: 7.5 and 10 cm Using Pythagoras' theorem: 7.52+102 = 156.25 Its square root: 12.5 cm Thus: 4*12.5 = 50 cm which is the perimeter of the rhombus Note: area of any quadrilateral whose diagonals are perpendicular is 0.5*product of their diagonals
What is the perimeter of a rhombus whose area is 30 square cm and whose largest diagonal is 12 cm showing work?
Let the other diagonal be x If: 0.5*12*x = 30 then x = 60/12 => x = 5 The rhombus has four interior right angle triangles with lengths of 6 cm and 2.5 cm Using Pythagoras each equal sides of the rhombus works out as 6.5 cm Perimeter: 4*6.5 = 26 cm
What is the perimeter of a rhombus whose diagonals add up to 21 cm and has an area of 54 square cm showing work?
Let the diagonals be x and y:- If: x+y = 21 then y = 21-x If: 0.5xy = 54 then 0.5x(21-x) = 54 => 21x -x squared -108 = 0 Solving the above quadratic equation: x = 12 or x = 9 The rhombus will then consist of 4 right angle triangles with base 4.5 and height 6 Using Pythagoras' theorem their hypotenuses are 7.5 cm Perimeter: 4*7.5 = 30 cm
What is the perimeter of a rhombus when its diagonals add up to 24.5 cm and has an area of 73.5 square cm showing work?
Let the diagonals be x and y:- If: x+y = 24.5 then y = 24.5-x If: 0.5xy = 73.7 then 0.5x(24.5-x) = 73.5 So: 24.5x -x^2 -147 = 0 Solving the quadratic equation: x = 14 or x = 10.5 The rhombus will then consist of 4 right angle triangles of base 5.25 and height 7 Using Pythagoras: 5.25^2+7^2 = 76.5625 and its square root is 8.75 Therefore the perimeter of the rhombus: 4*8.75 = 35 cm
What is the perimeter of a rhobus when one of its diagonals is 12 cm and has an area of 54 square cm showing work?
Let the other diagonal be x:- If: 0.5*x*12 = 54 Then: x = 54/6 => 9 The rhombus will consist of 4 right angles: base 4.5 cm and height 6 cm Using Pythagoras: hypotenuses = 7.5 cm Therefore perimeter: 4*7.5 = 30 cm
Graph showing lengths proportional to ammounts?
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What is the perimeter of a rhombus whose diagonals add up to 41 cm and has an area of 210 square cm showing all work with final answer?
Double the area then find two number that have a sum of 41 and a product of 420:- If: x+y = 41 Then: y = 41-x If: xy = 420 Then: x(41-x) = 420 So: 41x -x^2 - 420 = 0 Solving the above quadratic equation: x = 21 or x = 20 meaning y is 20 The rhombus will then have 4 right angle triangles with sides of 10.5 and 10 Using Pythagoras' theorem: 10.5^2 + 10^2 = 210.25 and its square root is 14.5 Therefore the perimeter is: 4*14.5 = 58 cm Check: 0.5*21*20 = 210 square cm
How many triangles make a rhombus?
Two equilateral triangles can form a rhombus- it can also be formed by using a higher number of isosceles triangles.
