Ask a question

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

how to i set up the problem, and how do i work out the problem

1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Pierce O. | Graduate Mathematics Student, Will Tutor Any Math SubjectGraduate Mathematics Student, Will Tutor...
4.7 4.7 (6 lesson ratings) (6)
Hi Brynn,
The shape of a basketball court is a rectangle, and we know that the perimiter of a rectangle is given by
where l is the length and w is the width. Since we are given P = 114, we have
If the length is 6 meters longer than twice the width, then
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.