Dimensions of a RectangleDate: 8/26/96 at 0:14:47 From: Anonymous Subject: Area of a Rectangle A rectangle is three times as long as it is wide. If its length and width are both increased by 3 m, its area is increased by 81 m squared. Find its original dimensions. I understand that the width would be labeled "w", and each length would be labeled "3w". Date: 8/30/96 at 13:0:41 From: Doctor Jerry Subject: Re: Area of a Rectangle Good first step! The next step is to use w and 3w in expressing the given sentences as equations. For example, if length and width are both increased by 3 meters, then the new length and width are w+3 and 3w+3. Further, since the area is increased by 81 meters, the new area minus the old area is 81. The old area is w*(3w); the new area is (w+3)*(3w+3). Putting all of this together, (w+3)*(3w+3)-w*(3w)=81. After simplifying this equation you will find that w = 6. Does this fit? Well, original rectangle is 6 by 18, with area 108. If length and width are increased by 3, new rectangle is 9 by 21. The area of new rectangle is 189. 189-108 = 81. Everything checks. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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