document.write( "Question 151018: A RECTANGLE IS 4 TIMES AS LONG AS IT IS WIDE A SECOND RECTANGLE IS 5 CENTIMETERS LONGER AND 2 CENTIMETERS WIDER THAN THE FIRST. THE AREA OF THE SECOND RECTANGLE IS 270 SQUARE CENTIMETERS GREATER THAN THE FIRST. WHAT ARE THE DIMENSIONS OF THE ORIGINAL RECTANGLE \n" ); document.write( "

Algebra.Com's Answer #111006 by jojo14344(1513) $\"\"$ $\"About$

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We need to remember the following,
\n" ); document.write( "1st rectangle (original) $\"R%5B1%5D\"$ is designated below,
\n" ); document.write( " $\"highlight%28A%5B1%5D%29rea\"$ , $\"highlight%28L%5B1%5D%29ength\"$ , & $\"highlight%28W%5B1%5D%29idth\"$
\n" ); document.write( "2nd rectangle, $\"R%5B2%5D\"$
\n" ); document.write( " $\"highlight%28A%5B2%5D%29rea\"$ , $\"highlight%28L%5B2%5D%29ength\"$ , & $\"highlight%28W%5B2%5D%29idth\"$
\n" ); document.write( "In $\"R%5B1%5D\"$ : $\"L%5B1%5D=4W%5B1%5D\"$ ---> length 4 times its width
\n" ); document.write( "So, $\"A%5B1%5D=L%5B1%5D%2AW%5B1%5D=4W%5B1%5D%2AW%5B1%5D\"$ ---> $\"A%5B1%5D=4W%5B1%5D%5E2\"$ ----------> eqn 1
\n" ); document.write( ".
\n" ); document.write( "In $\"R%5B2%5D\"$ : $\"L%5B2%5D=L%5B1%5D%2B5cm\"$ ---> 5 cm longer
\n" ); document.write( "Also, $\"W%5B2%5D=W%5B1%5D%2B2\"$ ----------> 2 cm wider
\n" ); document.write( "So, $\"A%5B2%5D=%28L%5B1%5D%2B5%29%28W%5B1%5D%2B2%29\"$ -------------------------------------------->A
\n" ); document.write( "And we have to remember, $\"A%5B2%5D=A%5B1%5D%2B270cm%5E2\"$ ---> greater than 270sqcm-->B
\n" ); document.write( "Plug in eqn 1 in this condition: $\"A%5B2%5D=4W%5B1%5D%5E2%2B270cm%5E2\"$ ---------------->C
\n" ); document.write( "Therefore, equating A & C,
\n" ); document.write( " $\"%28L%5B1%5D%2B5%29%28W%5B1%5D%2B2%29=4W%5B1%5D%5E2%2B270\"$
\n" ); document.write( "Remember in $\"R%5B1%5D\"$ that $\"L%5B1%5D=4W%5B1%5D\"$ & substitute:
\n" ); document.write( " $\"%284W%5B1%5D%2B5%29%28W%5B1%5D%2B2%29=4W%5B1%5D%5E2%2B270\"$
\n" ); document.write( " $\"cross%284W%5B1%5D%5E2%29%2B13W%5B1%5D%2B10=cross%284W%5B1%5D%5E2%29%2B270\"$
\n" ); document.write( " $\"13W%5B1%5D=270-10\"$ ------> $\"W%5B1%5D=260%2F13\"$ ---> $\"W%5B1%5D=20cm\"$ ---> ORIG. WIDTH
\n" ); document.write( "We know $\"L%5B1%5D=4W%5B1%5D=4%2A20cm\"$ ------------> $\"L%5B1%5D=80cm\"$ ----> ORIG LENGTH
\n" ); document.write( ".
\n" ); document.write( "For checking & verification,
\n" ); document.write( " $\"A%5B1%5D=L%5B1%5D%2AW%5B1%5D=80%2A20=1600cm\"$
\n" ); document.write( " $\"A%5B2%5D=%28L%5B1%5D%2B5%29%28W%5B1%5D%2B2%29=%2880%2B5%29%2820%2B2%29=1870cm\"$
\n" ); document.write( "This satisfy condition B above -----> $\"A%5B2%5D\"$ is 270cm greater than $\"A%5B1%5D\"$
\n" ); document.write( "1870-1600=270cm
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo\r
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