Question 641835: I need help figuring out an equation for: the width of a rectangular deck is 5 yds more than twice it's length. The perimeter is 76 yds. What are the width and length of the deck
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let L = length of rectangular deck
Let W = width of rectangular deck
From the statement, " the width is 5 yds more than twice the length," we write
(1) W = 2*L + 5
Using the formula for the perimeter, p, of a rectangle, we have
(2) p = 2*(L + w)
Substitute (1) for w into (2), results with
(3) p = 2*(L + 2*L + 5)
Simplify (3) yields
(4) p = 10 + 6*L
The problem states that p = 76, therefore
(5) 6*L +10 = 76 or
(6) 6*L = 66 and
(7) L = 11
Using (1) we get
(8) W = 27
Are we correct?
Is (2L + 2W = 76)?
Is (22 + 54 = 76)?
Is (76 = 76)? Yes
Answer: The width and length of the deck are 27 yards and 11 yards, respectively.
Comment: We usually consider the length being "longer" than the width, but mathematically it doesn't make any difference. So don't be confused by what I consider a poor choice of dimensions in this problem.
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