document.write( "Question 636311: A rectangle 15cmx30cm is increased on all sides by the same amount. It's area is increased by 144cm^2. By how much is each dimension increased? \n" ); document.write( "

Algebra.Com's Answer #400960 by Maths68(1474) $\"\"$ $\"About$

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\n" ); document.write( "Increase on all sides = x \r
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\n" ); document.write( "\n" ); document.write( "Area of rectangle = length * width
\n" ); document.write( "A=L*W
\n" ); document.write( "A=15*30
\n" ); document.write( "A=450
\n" ); document.write( "After Increase
\n" ); document.write( "A=450+144
\n" ); document.write( "A=594
\n" ); document.write( "Length = 30+x
\n" ); document.write( "Width = 15+x\r
\n" ); document.write( "\n" ); document.write( "594=(15+x)(30+x)
\n" ); document.write( "594=450+15x+30x+4x^2
\n" ); document.write( "594=450+45x+x^2
\n" ); document.write( "594-450=45x+x^2
\n" ); document.write( "144=45x+x^2
\n" ); document.write( "x^2+45x-144=0
\n" ); document.write( "x^2+48x-3x-144=0
\n" ); document.write( "x(x+48)-3(x+48)=0
\n" ); document.write( "(x-3)(x+48)=0
\n" ); document.write( "x-3=0 or x+48=0
\n" ); document.write( "x=3 or x=-48 (unacceptable)
\n" ); document.write( "x=3\r
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\n" ); document.write( "\n" ); document.write( "Each dimension increased by 3cm
\n" ); document.write( "Length = 30+x = 30+3 = 33cm
\n" ); document.write( "Width = 15+x = 15+3 = 18cm\r
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