document.write( "Question 316479: Two squares have total area 85 cm^2 and total perimeter 52 cm. what is the area in cm^2 of the large square ?
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Algebra.Com's Answer #226674 by ankor@dixie-net.com(22740)\"\" \"About 
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Two squares have total area 85 cm^2 and total perimeter 52 cm.
\n" ); document.write( " what is the area in cm^2 of the large square ?
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\n" ); document.write( "Let x = side of the large square
\n" ); document.write( "then
\n" ); document.write( "x^2 = it's area
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\n" ); document.write( "Let y = side of small square
\n" ); document.write( "then
\n" ); document.write( "y^2 = it's area
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\n" ); document.write( "\"Two squares have total area 85 cm^2\"
\n" ); document.write( "x^2 + y^2 = 85
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\n" ); document.write( "\" total perimeter 52 cm.\"
\n" ); document.write( "4x + 4y = 52
\n" ); document.write( "simplify, divide by 4
\n" ); document.write( "x + y = 13
\n" ); document.write( "y = (13-x)
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\n" ); document.write( "replace y with (13-x) in the total area equation
\n" ); document.write( "x^2 + (13-x)^2 = 85
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + 169 - 26x + x^2 = 85
\n" ); document.write( "Combine as a quadratic equation
\n" ); document.write( "2x^2 - 26x + 169 - 85 = 0
\n" ); document.write( "2x^2 - 26x + 84 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(2x-12)(x-7) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 7
\n" ); document.write( "and
\n" ); document.write( "2x = 12
\n" ); document.write( "x = 6
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\n" ); document.write( "Area of the larger square: 7^2 = 49 sq/cm
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\n" ); document.write( "Check solution
\n" ); document.write( "y = 13-7
\n" ); document.write( "y = 6 cm
\n" ); document.write( "then 6^2 = 36cm is the small square area
\n" ); document.write( "total area: 49 + 36 = 85
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\n" ); document.write( "Check the perimeter
\n" ); document.write( "49 + 36 = 85;
\n" ); document.write( "4(7) + 4(6) = 52\r
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