document.write( "Question 1175842: Hi
\n" ); document.write( "The total perimeter of two squares of different sizes is 68cm. The total area of both squares 157 cm squared. What is the length of the bigger square.\r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #801541 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+highlight%2811cm%29\"$
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\n" ); document.write( "\n" ); document.write( "The workout:
\n" ); document.write( "Let $\"s%5B1%5D\"$ and $\"s%5B2%5D\"$ be the side lengths of the two squares
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\n" ); document.write( "\n" ); document.write( "Start with two equations
\n" ); document.write( " $\"+4s%5B1%5D+%2B+4s%5B2%5D+=+68+\"$ ---> $\"+s%5B1%5D+%2B+s%5B2%5D+=+17+\"$
\n" ); document.write( " $\"+s%5B1%5D%5E2+%2B+s%5B2%5D%5E2+=+157+\"$
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\n" ); document.write( "\n" ); document.write( "From here, substitute $\"s%5B1%5D+=+17-s%5B2%5D\"$ from the top eqn into the bottom:\r
\n" ); document.write( "\n" ); document.write( " $\"+%2817-s%5B2%5D%29%5E2+%2B+s%5B2%5D%5E2+=+157+\"$
\n" ); document.write( "Simplify, and factor
\n" ); document.write( " $\"+2s%5B2%5D%5E2+-34s%5B2%5D+%2B+132+=+0+\"$
\n" ); document.write( " $\"+s%5B2%5D%5E2+-+17s%5B2%5D+%2B+66+=+0+\"$
\n" ); document.write( " $\"+%28s%5B2%5D-11%29%28s%5B2%5D-6%29+=+0+\"$ \r
\n" ); document.write( "\n" ); document.write( "So $\"+s%5B2%5D+=+11+\"$ --> $\"+s%5B1%5D+=+6+\"$
\n" ); document.write( "or $\"+s%5B2%5D+=+6+\"$ --> $\"+s%5B1%5D+=+11\"$ <<< same answer, $\"s%5B1%5D\"$ is simply the larger square for this solution\r
\n" ); document.write( "\n" ); document.write( "---
\n" ); document.write( "Check: 4*11 + 4*6 = 44 + 24 = 68
\n" ); document.write( " 11^2 + 6^2 = 121 + 36 = 157
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