document.write( "Question 157074: Solve the problem. The perimeter of a rectangle is 62 m. If the width were doubled and the length were increased by 21 m, the perimeter would be 120 m. What are the length and width of the rectangle? \n" ); document.write( "
Algebra.Com's Answer #115814 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The perimeter of a rectangle is 62 m. If the width were doubled and the length
\n" ); document.write( " were increased by 21 m, the perimeter would be 120 m. What are the length and
\n" ); document.write( " width of the rectangle?
\n" ); document.write( ";
\n" ); document.write( "Write an equation for each statement, simplify as much as you can:
\n" ); document.write( ":
\n" ); document.write( "\"The perimeter of a rectangle is 62 m.\"
\n" ); document.write( "2L + 2W = 62
\n" ); document.write( "Simplify, divide equation by 2:
\n" ); document.write( "L + W = 31
\n" ); document.write( "L = (31-W); use for substitution
\n" ); document.write( ":
\n" ); document.write( "\"If the width were doubled and the length were increased by 21 m, the perimeter would be 120 m.\"
\n" ); document.write( "2(2W) + 2(L+21) = 120
\n" ); document.write( "4W + 2L + 42 = 120
\n" ); document.write( "4W + 2L = 120 - 42
\n" ); document.write( "4W + 2L = 78
\n" ); document.write( "Simplify divide by 2
\n" ); document.write( "2W + L = 39
\n" ); document.write( ":
\n" ); document.write( "Using the 1st equation, substitute (31-W) for L
\n" ); document.write( "2W + (31-W) = 39
\n" ); document.write( "2W - W = 39 - 31
\n" ); document.write( "W = 8 m is the original width
\n" ); document.write( "then
\n" ); document.write( "L = 31 - 8
\n" ); document.write( "L = 23 is the original length
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "\"If the width were doubled and the length were increased by 21 m, the perimeter would be 120 m.\"
\n" ); document.write( "New rectangle dimensions: 44 by 16
\n" ); document.write( "2(16) + 2(44) = 120; confirms our solutions\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );