document.write( "Question 987728: The area of a rectangle is 50, and its diagonal is sqrt(125). Find its dimensions and perimeter. \n" ); document.write( "
Algebra.Com's Answer #608471 by macston(5194)\"\" \"About 
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\n" ); document.write( "L=length; W=width; A=area; D=diagonal
\n" ); document.write( ".
\n" ); document.write( "LW=A
\n" ); document.write( "LW=50
\n" ); document.write( "L=50/W\r
\n" ); document.write( "\n" ); document.write( ".
\n" ); document.write( "L^2+W^2=D^2
\n" ); document.write( "(50/W)^2+W^2=(sqrt(125))^2
\n" ); document.write( "2500/W^2+W^2=125 Multiply each side by W^2
\n" ); document.write( "2500+W^4=125W^2
\n" ); document.write( "W^4-125W^2+2500=0
\n" ); document.write( "Let X=W^2:
\n" ); document.write( "X^2-125X+2500=0
\n" ); document.write( "(X-25)(X-100)=0
\n" ); document.write( "(X-25=0) OR (X-100=0)
\n" ); document.write( "{X=25 OR X=100 Substitute W^2 for X.
\n" ); document.write( "W^2=25 OR W^2=100
\n" ); document.write( "W=5 or W=10
\n" ); document.write( "ANSWER 1: The width is 5 or 10 units.
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\n" ); document.write( "If W=5 units:
\n" ); document.write( "L=50/W=50/5=10 units
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\n" ); document.write( "If W=10 units:
\n" ); document.write( "L=50/W=50/10=5 units
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\n" ); document.write( "ANSWER (DIMENSIONS):
\n" ); document.write( "Length is 10 units and width is 5 units,
\n" ); document.write( "or width is 10 units and length is 5 units.
\n" ); document.write( ".
\n" ); document.write( "Perimeter is same in both cases:
\n" ); document.write( "Perimeter=2(L+W)=2(10+5)=2(15)=30 units
\n" ); document.write( "ANSWER (PERIMETER): The perimeter is 30 units.\r
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