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What is the perimeter, in units, of a rhombus if its area is 120 square units and one diagonal is 10 units?

SmartMathMan  Dec 5, 2017
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The area  of a rhombus  =   product of the diagonals / 2

 

So

 

120  =   (10) D  / 2

 

120  = 5 D   divide both sides by 5

 

24  = D    =  the other diagonal

 

And the diagonals bisect each other......and these bisected diagonals form legs of a right triangle  and the side of the rhombus  forms the hypotenuse

 

So....the legs are  10/2  and 24/2  =   5   and 12

 

And by the Pythagorean Theorem.....

 

5^2 + 12^2  =  side^2

 

√ [ 5^2 + 12^2 ]  = side

 

√  169  =  side

 

13  = side

 

And since there are 4 sides....the perimeter is 4 * 13  =   52 units

 

 

 

cool cool cool

CPhill  Dec 5, 2017

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