document.write( "Question 1192931: A 44 cm piece of wire is cut and 2 squares are formed. The total are of both squares is 65 cm2. What’s the perimeter of each square? \n" ); document.write( "
Algebra.Com's Answer #824883 by Theo(13342)\"\" \"About 
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let x = the length of one side of one of the squares.
\n" ); document.write( "let y = the length of one side of the other square.
\n" ); document.write( "the area of both squares is given by the equation x^2 + y^2 = 65
\n" ); document.write( "the perimeter of both squares is given by the equation 4 * (x + y) = 44
\n" ); document.write( "in the second equation, solve for x + y to get:
\n" ); document.write( "x + y = 11
\n" ); document.write( "in that equation, solve for y to get:
\n" ); document.write( "y = 11 - x\r
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\n" ); document.write( "\n" ); document.write( "in the first equation, replace y with (11 - x) to get:
\n" ); document.write( "x^2 + y^2 = 65 becomes x^2 + (11-x)^2 = 65
\n" ); document.write( "simplify to get:
\n" ); document.write( "2x^2 + 121 -22 * x = 65
\n" ); document.write( "order the terms in descending order of degree to get:
\n" ); document.write( "2x^2 - 22 * x + 121 = 65
\n" ); document.write( "subtract 65 from both sides of the equation to get:
\n" ); document.write( "2x^2 - 22x + 56 = 0
\n" ); document.write( "divide both sides of the equation by 2 to get:
\n" ); document.write( "x^2 - 11x + 28 = 0
\n" ); document.write( "factor to get:
\n" ); document.write( "(x - 4) * (x - 7) = 0
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 4 or x = 7\r
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\n" ); document.write( "\n" ); document.write( "when x = 4, x^2 + y^2 = 65 becomes 16 + y^2 = 65.
\n" ); document.write( "solve for y^2 to get y^2 = 65 - 16 = 49
\n" ); document.write( "solve for y to get y = 7
\n" ); document.write( "when x = 7, x^2 + y^2 = 65 becomes 49 + y^2 = 65
\n" ); document.write( "solve for y^2 to get y^2 = 65 - 49 = 16
\n" ); document.write( "solve for y to get y = 4\r
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\n" ); document.write( "\n" ); document.write( "your solution is therefore:
\n" ); document.write( "x = 4 and y = 7 or x = 7 and y = 4\r
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\n" ); document.write( "\n" ); document.write( "to confirm, replace x and y in the original equations to get:
\n" ); document.write( "x^2 + y^2 = 65 becomes 4^2 + 7^2 = 65 which becomes 16 + 49 = 65 which becomes 65 = 65, confirming the value of x and y are good in the first equation.
\n" ); document.write( "4x + 4y = 44 becomes 4*4 + 4*7 = 44 which becomes 16 + 28 = 44 which becomes 44 = 44, confirming the value of x and y are good in the second equation.
\n" ); document.write( "this works with x = 4 and y = 7.
\n" ); document.write( "it also works with x = 7 and y = 4.\r
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\n" ); document.write( "\n" ); document.write( "the solution is that the perimeter of one of the squares is 16 and the perimeter of the other square is 28.\r
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\n" ); document.write( "\n" ); document.write( "here's what the solution looks like graphically.\r
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