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Students in an environmental club are planning a garden with four rectangular plots of land separated by stone paths, as shown. The stone paths will have the same width.

 16 ft x 8 ft

 

a. The students plan to cover 80 square feet of path with stone. Write and solve an equation to find the width of the paths.

 

b. In part (a) you used one solution of an equation to find your answer. Explain how you chose which solution to use.

GAMEMASTERX40  Apr 7, 2018
edited by GAMEMASTERX40  Apr 7, 2018
edited by GAMEMASTERX40  Apr 7, 2018
edited by GAMEMASTERX40  Apr 7, 2018
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4+0 Answers

 #1
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What are the dimensions of the rectangles? 18 ft x ? ft (can't read the depth on RHS).

Guest Apr 7, 2018
 #2
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Sorry, the pic was blurry. The dimensions of the rectangle are 16 ft and 8 ft.

GAMEMASTERX40  Apr 7, 2018
 #3
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area of stone path in sq ft   =   16x  +  8x  -  x2

 

area of stone path in sq ft   =   24x - x2        Plug in  80  for the area of the stone path.

 

80  =   24x - x2        Add  x2  to both sides of the equation

 

x2 + 80   =   24x      Subtract  24x  from both sides.

 

x2 - 24x + 80   =   0       What two numbers add to  -24  and multiply to  80  ?  -20  and -4 .

 

(x - 20)(x - 4)   =   0       Set each factor equal to  0  and solve for  x .

 

x - 20  =  0         or        x - 4  =  0

 

x  =  20              or        x  =  4

 

The width of the paths must be less than the lengths of the sides of the big rectangle,

so  x  must be less than  16 , and  x  must be less than  8 .

 

Since  20  is too large for the width of the paths, the only solution is  x  = 4

hectictar  Apr 7, 2018
 #4
avatar+632 
+2

Thanks!

GAMEMASTERX40  Apr 7, 2018

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