document.write( "Question 816186: how to find the diagonals of a rhombus with area and side \n" ); document.write( "

Algebra.Com's Answer #491587 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( " $\"area=2xy\"$
\n" ); document.write( " $\"side%5E2=x%5E2%2By%5E2\"$
\n" ); document.write( " $\"area%2Bside%5E2=x%5E2%2B2xy%2By%5E2=%28x%2By%29%5E2\"$
\n" ); document.write( "Making
\n" ); document.write( " $\"b=-sqrt%28area%2Bside%5E2%29=-%28x%2By%29\"$ and
\n" ); document.write( " $\"c=area%2F2=xy\"$ ,
\n" ); document.write( "we can write the equation
\n" ); document.write( " $\"z%5E2%2Bbz%2Bc=0\"$ .
\n" ); document.write( "The solutions to that equation will be $\"x\"$ and $\"y\"$ ,
\n" ); document.write( "and the diagonals of the rhombus are $\"2x\"$ and $\"2y\"$ .
\n" ); document.write( "
\n" ); document.write( "For example, if $\"side=65\"$ and $\"area=2016\"$ in some units and the corresponding square units respectively,
\n" ); document.write( "

and
\n" ); document.write( " $\"c=2016%2F2=1008\"$ .
\n" ); document.write( "Solving the equation
\n" ); document.write( " $\"z%5E2-79z%2B1008=0\"$
\n" ); document.write( "either by factoring it into
\n" ); document.write( " $\"%28z-16%29%28z-63%29=0\"$ or by applying the quadratic formula
\n" ); document.write( "

and $\"z=63\"$ ,
\n" ); document.write( "for a rhombus with diagonals measuring $\"2%2A16=32\"$ and $\"2%2A63=126\"$ \n" ); document.write( "

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