document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198910>Question 198910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The original dimensions of a rectangle were 15cm by 20cm. When both dimensions were decreased by the same amount, the area of the new rectangle is half the area of the original rectangle. Find the dimensions of the new rectangle. Use let statements </SPAN>\n" );
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document.write( "the original dimensions are 15cm and 20cm<BR>\n" );
document.write( "let the dimensions are decreased by x amount<BR>\n" );
document.write( "after decreasing the dimensions are 15-x,20-x<BR>\n" );
document.write( "area of the original rectangle=15*20=300cm^2<BR>\n" );
document.write( "now the area of the new recatngle=(15-x)*(20-x)<BR>\n" );
document.write( "according to the problem<BR>\n" );
document.write( "area of the new rectangle=half the area of the original rectangle<BR>\n" );
document.write( " area of the new rectangle=1/2*area of the original rectangle<BR>\n" );
document.write( "(15-x)(20-x)=1/2*300<BR>\n" );
document.write( "(15-x)(20-x)=300/2<BR>\n" );
document.write( "(15-x)(20-x)=150<BR>\n" );
document.write( "15*(20-x)-x*(20-x)=150<BR>\n" );
document.write( "[15*20-15*x]-[x*20-x*x]=150<BR>\n" );
document.write( "[300-15x]-[20x-x^2]=150<BR>\n" );
document.write( "300-15x-20x+x^2=150<BR>\n" );
document.write( "300-35x+x^2=150<BR>\n" );
document.write( "x^2-35x+300=150<BR>\n" );
document.write( "x^2-35x+300-150=0<BR>\n" );
document.write( "x^2-35x+150=0<BR>\n" );
document.write( "x^2-5x-30x+150=0<BR>\n" );
document.write( "x(x-5)-30(x-5)=0<BR>\n" );
document.write( "(x-5)(x-30)=0<BR>\n" );
document.write( "x-5=0<BR>\n" );
document.write( "x=5<BR>\n" );
document.write( "x-30=0<BR>\n" );
document.write( "x=30<BR>\n" );
document.write( "now we take x=5<BR>\n" );
document.write( "the dimensions of the new rectangle=15-x,20-x<BR>\n" );
document.write( "=15-5,20-5<BR>\n" );
document.write( "=10,15<BR>\n" );
document.write( "now we take x=30<BR>\n" );
document.write( "the dimensions of the new rectangle=15-x,20-x<BR>\n" );
document.write( "=15-30,20-30<BR>\n" );
document.write( "=-15,-10<BR>\n" );
document.write( "in this problems we always take positive values<BR>\n" );
document.write( " so the dimensions of the new rectangle were 10cm,15cm </SPAN>\n" );
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