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Other than what? It really all depends on what is given. For example:

  • If you know the length of one diagonal, the other is just as long.
  • If you know the length and width of the rectangle, use Pythagoras' formula for the diagonal.
  • If you know one of the sides of the rectangle, and an angle, use some basic trigonometry to find the diagonal.
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Q: Are there another formulae in solving th diagonals of the rectangles?
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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


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Providing that it is a regular polygon then let its sides be x: So: 0.5*(x2-3x) = 464 diagonals Then: x2-3x-928 = 0 Solving the equation: x = 32 sides Total sum of interior angles: 30*180 = 5400 degrees Each interior angle: (5400+360)/180 = 168.75 degrees


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Let the sides be n and use the formula for the diagonals of a polygon:- If: 0.5*(n^2 -3n) = 90 Then: n^2 -3n -180 = 0 Solving the above quadratic equation: n = -12 or n = 15 Therefore the polygon has 15 sides


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Formula: 0.5*(n2-3n) = diagonals whereas n is the number of sides So if: 0.5*(n2-3n) = 54 Then: n2-3n-108 = 0 Solving the above quadratic equation gives n a value of -9 and 12 It has to be 12 which means it is a dodecagon polygon


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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