document.write( "Question 733236: The length of a rectangle is 3 times its width. The diagonal is 2 more than the length. Find the width of the rectangle.\r
\n" ); document.write( "\n" ); document.write( "please and thank you!((:
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #448371 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The length of a rectangle is 3 times its width.
\n" ); document.write( " The diagonal is 2 more than the length.
\n" ); document.write( " Find the width of the rectangle.
\n" ); document.write( ":
\n" ); document.write( "Let L = the Length
\n" ); document.write( "Let W = the width
\n" ); document.write( ";
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\"The length of a rectangle is 3 times its width.\"
\n" ); document.write( "L = 3W
\n" ); document.write( ":
\n" ); document.write( "\"The diagonal is 2 more than the length.\"
\n" ); document.write( "let c = the diagonal
\n" ); document.write( "then
\n" ); document.write( "c = (L+2)
\n" ); document.write( "or, since L = 3W we can write it
\n" ); document.write( "c = (3W+2)
\n" ); document.write( "The diagonal is the hypotenuse of the two right triangles
\n" ); document.write( "formed by the rectangle:
\n" ); document.write( ":
\n" ); document.write( "Using Pythag a^2 + b^2 = c^2
\n" ); document.write( "then we have:
\n" ); document.write( "(3W)^2 + W^2 = (3W+2)^2
\n" ); document.write( "FOIL
\n" ); document.write( "9W^2 + W^2 = 9W^2 + 6W + 6W + 4
\n" ); document.write( "10W^2 = 9W^2 + 12W + 4
\n" ); document.write( "Combine like terms on the left
\n" ); document.write( "10W^2 - 9W^2 - 12W - 4 = 0
\n" ); document.write( "W^2 - 12W - 4 = 0
\n" ); document.write( "solve this using the quadratic formula
\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "in this problem: x=w; a=1; b=-12; c=-4
\n" ); document.write( " \"w+=+%28-%28-12%29+%2B-+sqrt%28-12%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29+\"
\n" ); document.write( " \"w+=+%2812+%2B-+sqrt%28144%2B16+%29%29%2F2+\"
\n" ); document.write( "the reasonable solution
\n" ); document.write( " \"w+=+%2812+%2B+12.65%29%2F2+\"
\n" ); document.write( "w = \"24.65%2F2\"
\n" ); document.write( "w = 12.325 is the width
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "You can check this; find the hypotenuse with legs of 3(12.325)
\n" ); document.write( "and 12.325.
\n" ); document.write( " It should be 2 units more than the Length which is 3 times the width \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );