Greenwood press
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book-20600
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PERIMETER A carpenter or artist uses the concept of perimeter to build frames for pictures and paintings. Rectangular pen with length l and width w. width is 20 meters. If the width is 20 meters, and l = 40 − w, then the length is also 20 meters when the area of the rectangle is a maximum value. Therefore the ideal rectangular pen based on an existing amount of fencing is a square. However, if the farmer wants to build a pen that divides different animals, then the dimensions will have to be reconsidered. For example, suppose there are chickens and pigs in a pen that is evenly divided by a fence line. In this case, the dimensions of the most ideal pen would be determined by the equation 3w +2l = 80 to account for the added divider. The area of this pen is a = (40 − 1.5w)w = 40w − 1.5w 2 . A graph of this function shows that the area attains a maximum value when the width is 40/3 meters. If the width is 40/3 meters, and l = 40 − 1.5w, then the length of the fence should be 20 meters (40 − 1.5 • 40 3 ) when the area of the rectangle is a maximum value. In addition to building fences, the concept of perimeter is used in building race tracks. For example, in track and field, a 400-meter track represents the perimeter around two congruent semicircles, where the turns and straightaways are each one hundred meters. Building a track with these dimensions requires designers and engineers to determine the distance across the track between straightaways, which represents the diameter of the semicircles. Since the cir- cumference of a circle is π times its diameter, the circumference of a semicircle is one-half π times its diameter (c = 1 2 πd). Rearranging the variables in the equation can show that the diameter, d, of a semicircle is d = 2c π , where c is the circumference of the semicircle, which is the 100-meter turn of the track. The distance across the infield of a track is d = 2•100 π , which is approximately 63.662 meters. Download 1.81 Mb. Do'stlaringiz bilan baham: |
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