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if the perimeter of basketball court is 114 meters and the length is 6 meters longer then twice the width, what are the length and width

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1 Answer

Hi Brynn,
 
The shape of a basketball court is a rectangle, and we know that the perimiter of a rectangle is given by
 
2l+2w=P                
 
where l is the length and w is the width. Since we are given P = 114, we have
 
2l+2w=114
 
If the length is 6 meters longer than twice the width, then
 
l=6+2w
 
Now, substituting this back into 2l + 2w = 114, we have
 
2(6+2w)+2w = 114    (substitution)
 
12+4w+2w    = 114    (distribution)
 
12+6w           = 114    (add like terms)
 
Now we can solve for w. Taking 12 away from both sides leaves us with
 
6w = 101
 
and dividing by 6 yields the result
 
w = 17
 
Since we know that l = 6 + 2w, we have
 
l = 6 + 2(17)
 
  = 40
 
So the length is 40 and the width is 17.

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