SOLUTION: The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 206 feet, what is the area of the garden in square feet?
A factory is to be bui
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-> SOLUTION: The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 206 feet, what is the area of the garden in square feet?
A factory is to be bui
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Question 191521: The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 206 feet, what is the area of the garden in square feet?
A factory is to be built on a lot measuring 180 ft by 240 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory.
What must the width of the lawn be? Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website! first problem
per = 206 = (2*l) + (2*w) = 2( w + 9) + 2(w) = 2w + 18 + 2w = 4w +18
substr 18 from both sides
188 = 4w
divide each side by 4
w = 47
check per = 206 = 2 ( 47 + (47 + 9) ) = 206 ok
Area = l * w = 47 * ( 47 + 9) = 47 * 56 = 2632
problem 2
area = l * w = 180 * 240 = 43200
factory area is then 43200 / 2 = 21600 as is green belt area
factory dim are ( 180-2w) by (240 -2w)
factory area = l*w = (180-2w) * (240-2w)
21600=180 *240 -2*180*w -2*240*w +4w^2
21600 = 43200 -360w -480w +4w^2
subst 21600 both sides
0 = 21600 -840w +4w^2
factor 0= 4( w^2 -210 w +5400)
solve using quadratic formula
w = ( -(-210) +- sq rt ( (-210)^2 - 4 (1) (5400) ) ) /2 (1)
w= ( 210 +- 150 ) /2
w= 360/2=180 to big not realistic
or w = 60/2 = 30
this makes factory size (180-2*30) = 120 by (240 -2*30) = 180
checking 180 * 120 = 21600 ok
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