Area of an Inner RectangleDate: 01/19/2003 at 17:00:43 From: Jamie Subject: Word problem... When Fred and Wilma reached retirement, they were finally able to buy the house of their dreams. It had a 40 ft by 72 ft rectangular yard. Wilma cultivated 5/12 of the area in flowers, which she grew in an even border around the central grass area. Every morning Fred walked Dino around the central grass area inside the flowers. How many laps did he have to do to walk at least 1/4 mile? I don't understand where to start because I can't visualize what facts are essential in arriving the answer. Is it really important that Wilma cultivated 5/12 of the yard in flowers? Or should I begin with how many feet are in a mile? How would you even determine 5/12 of a 40 ft by 72 ft rectangular yard? Is the central grass area that Fred walks Dino around the entire yard? Or just the remaining fraction? Please help! Date: 01/20/2003 at 13:17:12 From: Doctor Ian Subject: Re: Word problem... Hi Jamie, It's critical the the border be _even_, i.e., have the same width everywhere: 72 - +---------------------+ x| | | - | +---------------+ | | | | | 40 | | | | - | +---------------+ | x| | | - +---------------------+ |--| |--| x x Now, what is the area of the border? We can divide it up into four rectangles: +--+------------------+ | | a | | | +---------------+ | | | |b | 40 | d| | | | +---------------+ | | | c | | +---------------------+ The areas of the rectangles a-d will be functions of x. For example, area(a) = (72 - 2x) * x Add them up, and they have to add up to 5/12 of the area of the whole yard: areas of a, b, c, d = (5/12) * (72 * 40) Solve this equation to find x, and that will tell you the dimensions of the inner rectangle. Is this enough to get started? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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