document.write( "Question 449030: Kumar walks around a rectangular field the length of which is twice its width. He then walks around another rectangular field half as wide but having the same perimeter as the first field. If the difference in area between the two fields is 432 m, find the length of the second field. \n" ); document.write( "
Algebra.Com's Answer #308956 by ankor@dixie-net.com(22740)\"\" \"About 
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Kumar walks around a rectangular field the length of which is twice its width.
\n" ); document.write( " He then walks around another rectangular field half as wide but having the same perimeter as the first field.
\n" ); document.write( " If the difference in area between the two fields is 432 m, find the length of the second field.
\n" ); document.write( ":
\n" ); document.write( "Let x = width of original field
\n" ); document.write( "then
\n" ); document.write( "2x = length of original field
\n" ); document.write( "and
\n" ); document.write( "2x + 2(2x) =
\n" ); document.write( "6x = perimeter of the original field
\n" ); document.write( "and
\n" ); document.write( "2x^2 = area of original field
\n" ); document.write( ":
\n" ); document.write( "L = length of the 2nd field
\n" ); document.write( "and
\n" ); document.write( ".5x = width of the 2nd field
\n" ); document.write( "and
\n" ); document.write( "2L + 2(.5x) =
\n" ); document.write( "2L + x = perimeter of the 2nd field
\n" ); document.write( "and
\n" ); document.write( ".5x*L = area of the 2nd field
\n" ); document.write( ":
\n" ); document.write( "Perimeter the same, therefore:
\n" ); document.write( "2L + x = 6x
\n" ); document.write( "2L = 6x - x
\n" ); document.write( "2L = 5x
\n" ); document.write( "L = \"5%2F2\"x
\n" ); document.write( "L = 2.5x
\n" ); document.write( ":
\n" ); document.write( "\"If the difference in area between the two fields is 432 m,\"
\n" ); document.write( "2x^2 - .5x*L = 432
\n" ); document.write( "Replace L with 2.5x
\n" ); document.write( "2x^2 - .5x(2.5x) = 432
\n" ); document.write( "2x^2 - 1.25x^2 = 432
\n" ); document.write( ".75x^2 = 432
\n" ); document.write( "x^2 = \"432%2F.75\"
\n" ); document.write( "x^2 = 576
\n" ); document.write( "x = \"sqrt%28576%29\"
\n" ); document.write( "x = 24 m the width of the original width
\n" ); document.write( "2(24) = 48 m the length of the original field
\n" ); document.write( "then
\n" ); document.write( "L = 2.5(24)
\n" ); document.write( "L = 60 m is the length of the 2nd field
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this
\n" ); document.write( "1st field 48 by 24, 2nd field: 60 by 12
\n" ); document.write( "Check solution by finding the perimeter of each
\n" ); document.write( "2(48) + 2(24) = 144
\n" ); document.write( "2(60) + 2(12) = 144, confirms our solution\r
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