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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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โˆ™ 2013-08-09 12:43:30
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Q: 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?
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Is the sum of the lengths of the diagonals of a polygon greater than the perimeter of the polygon?

I'm some cases yes while in others no :)

What is the perimeter of a rhombus when one diagonal is greater than the other diagonal by 10.5 cm and has an area of 67.5 square cm?

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