SOLUTION: the length of a rectangle is 13 centimeters less than six times its width. its area is 15. find the dimension of the rectangle.

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Question 539178: the length of a rectangle is 13 centimeters less than six times its width. its area is 15. find the dimension of the rectangle.
Answer by Mathpassionate(25) About Me  (Show Source):
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L = Length
W = Width
A = Area
P = Perimeter
Information provided:
L = 6W - 13
A = 15
P = ?

A = L*W
15 = (6W - 13)*W
15 = 6W^2 - 13W
6W^2 - 13W - 15 = 0

Using the quadratic formula:

x = (-b +- sqrt(b2 - 4ac) )/2a

Here we have:
b = -13
a = 6
c = -15

Then,

W = (-(-13) +- sqrt%28+13%5E2-4%2A6%2A%28-15%29%29)/(2*6)

W = (13 +- sqrt%28169+%2B360%29)/(12)
W = (13 +- sqrt%28529%29)/(12)
W = (13 +- 23)/(12)
W = (13 +- 23)/(12) (The negative value is ignored for dimensions)
W = (13 + 23)/(12)
W = 36/12
W = 3


Now, we substitute W = 3 into L = 6W - 13

L = 6W - 13
L = 6*3 - 13
L = 18 - 13
L = 5

We know that P = 2L + 2W

P = 2L + 2W
P = 2*5 + 2*3
P = 10 + 6
P = 16


The dimension of the rectangle is 16 cms, which is the answer.


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