Geometry The length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden. (a) Draw a diagram that gives a visual representation of the problem. (b) Write the equation for the perimeter y of the walkway in terms of x . (c) Use a graphing utility to graph the equation for the perimeter. (d) Determine the slope of the graph in part (c). For each additional one-meter increase in the width of the walkway, determine the increase in its perimeter.
Geometry The length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden. (a) Draw a diagram that gives a visual representation of the problem. (b) Write the equation for the perimeter y of the walkway in terms of x . (c) Use a graphing utility to graph the equation for the perimeter. (d) Determine the slope of the graph in part (c). For each additional one-meter increase in the width of the walkway, determine the increase in its perimeter.
Solution Summary: The author illustrates the visual representation of a rectangular garden of length and breadth.
Geometry The length and width of a rectangular garden are
15
meters and
10
meters, respectively. A walkway of width
x
surrounds the garden.
(a) Draw a diagram that gives a visual representation of the problem.
(b) Write the equation for the perimeter
y
of the walkway in terms of
x
.
(c) Use a graphing utility to graph the equation for the perimeter.
(d) Determine the slope of the graph in part (c). For each additional one-meter increase in the width of the walkway, determine the increase in its perimeter.
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