document.write( "Question 279050: Ok, there is a problem in my worksheet that gives me the following information:
\n" ); document.write( "Perimeter of the Rectangle: 68cm
\n" ); document.write( "Area of the Rectangle: 144sq. cm\r
\n" ); document.write( "\n" ); document.write( "and its asking for the length of the diagonal, how do i solve this? it does not give any dimensions (Width, Height)
\n" ); document.write( "If you can help me, id love it. Thank You
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #202972 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
gives me the following information:
\n" ); document.write( ":
\n" ); document.write( "Start by using L for Length, W for width
\n" ); document.write( ":
\n" ); document.write( "Perimeter of the Rectangle: 68cm
\n" ); document.write( "2L + 2W = 68
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "L + W = 34
\n" ); document.write( "or
\n" ); document.write( "W = (34-L)
\n" ); document.write( ":
\n" ); document.write( "Area of the Rectangle: 144sq. cm
\n" ); document.write( "L * W = 144
\n" ); document.write( "Substitute (34-L) for W
\n" ); document.write( "L * (34-L) = 144
\n" ); document.write( "34L - L^2 = 144
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "-L^2 + 34L - 144 = 0
\n" ); document.write( "We have to 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 equation: x=L; a=-1; b=34; c=-144
\n" ); document.write( "\"L+=+%28-34+%2B-+sqrt%2834%5E2-4%2A-1%2A-144+%29%29%2F%282%2A-1%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"L+=+%28-34+%2B-+sqrt%281156-576+%29%29%2F%28-2%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"L+=+%28-34+%2B-+sqrt%28580+%29%29%2F%28-2%29+\"
\n" ); document.write( "Two solutions
\n" ); document.write( "\"L+=+%28-34+%2B+24.083%29%2F%28-2%29+\"
\n" ); document.write( "L = \"%28-9.917%29%2F%28-2%29\"
\n" ); document.write( "L = +4.958
\n" ); document.write( "and
\n" ); document.write( "\"L+=+%28-34+-+24.083%29%2F%28-2%29+\"
\n" ); document.write( "L = \"%28-58.083%29%2F%28-2%29\"
\n" ); document.write( "L = +29.0415
\n" ); document.write( ":
\n" ); document.write( "the larger 29.0415 cm is the length
\n" ); document.write( "the smaller 4.958 cm is the width
\n" ); document.write( ":
\n" ); document.write( "Check our solution by finding the perimeter with a calc
\n" ); document.write( "2(29.0415) + 2(4.958) = 67.999 ~ 68
\n" ); document.write( ":
\n" ); document.write( "and its asking for the length of the diagonal, now we have the dimensions:
\n" ); document.write( "Use pythag for this: c = \"sqrt%28a%5E2+%2B+b%5E2%29\",
\n" ); document.write( ":
\n" ); document.write( "c = \"sqrt%2829.0415%5E2+%2B+4.958%5E2%29\"
\n" ); document.write( "c = 29.462 is the diagonal \n" ); document.write( "
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