515 /www/nrich/html/content/97/06/six6/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) is the width decreased by ?</p> <mdo:image src="rect.gif" align="texttop" border="0" alt=""></mdo:image> <br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>The area of the original rectangle was wb.</p> <mdo:image align="texttop" alt="" border="0" src="area.gif"></mdo:image><br></br> <p>The area of the altered rectangle is pw x 1.1b.</p> <mdo:image align="texttop" alt="" border="0" src="area1.gif"></mdo:image><br></br> <p>Since the two areas are equal,</p> <p>1.1 pwb = wb</p> <p>so</p> <p>1.1 p = 1</p> <p>so p = 1/1.1 = 10/11<br></br> So the width is 10/11 of its original value, so it has been decreased by 1/11, which as a percentage is 9 and 1/11 %, or 9.09 % to 2.d.p.</p></mdoxml> 2 4 0 0 0 1 0 If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) is the width decreased by ? Fractions, Decimals, Percentages, Ratio and Proportion Calculating with percentages Fractions, Decimals, Percentages, Ratio and Proportion Percentages Measures and Mensuration Area