document.write( "Question 1011929: Quadrilateral PQRS has right angles at P and R. If PQ=9, PS=12, and QR=10, find RS. Thanks. \n" ); document.write( "

Algebra.Com's Answer #627790 by KMST(5328) $\"\"$ $\"About$

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In quadrilateral $\"PQRS\"$ ,
\n" ); document.write( "vertex $\"P\"$ is adjacent to vertices $\"Q\"$ and $\"S\"$ .
\n" ); document.write( "Since there is a right angle at $\"P\"$ ,
\n" ); document.write( "triangle $\"PQS\"$ is a right triangle with hypotenuse $\"QS\"$ ,
\n" ); document.write( "and legs $\"PQ=9\"$ and $\"PS=12\"$ .
\n" ); document.write( "Using the Pytahagorean theorem, we can find hypotenuse $\"QS\"$ :
\n" ); document.write( " $\"QS%5E2=PQ%5E2%2BPS%5E2\"$
\n" ); document.write( " $\"QS%5E2=9%5E2%2B12%5E2=81%2B144=225\"$ and $\"QS=sqrt%28225%29=15\"$ .
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\n" ); document.write( "In quadrilateral $\"PQRS\"$ ,
\n" ); document.write( "vertex $\"R\"$ is adjacent to vertices $\"Q\"$ and $\"S\"$ .
\n" ); document.write( "Since there is a right angle at $\"R\"$ ,
\n" ); document.write( "triangle $\"RQS\"$ is a right triangle with hypotenuse $\"QS=15\"$ ,
\n" ); document.write( "and legs $\"QR=10\"$ and $\"PS\"$ .
\n" ); document.write( "Using the Pytahagorean theorem, we can find leg $\"PS\"$ :
\n" ); document.write( " $\"QS%5E2=QR%5E2%2BPS%5E2\"$
\n" ); document.write( " $\"225=10%5E2%2BPS%5E2\"$ ---> $\"225=100%2BPS%5E2\"$ ---> $\"225-100=PS%5E2\"$ .
\n" ); document.write( "So, $\"PS%5E2=125\"$ ---> $\"PS=sqrt%28125%29\"$ }---> $\"highlight%28PS=5sqrt%285%29%29\"$ .
\n" ); document.write( "If you want an approximate measure, $\"highlight%28PS=about11.18%29\"$ (rounded).
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