<PRE><B>Question 539178</B>
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( 13^2-4*6*(-15))}}})/(2*6)


W = (13 +- {{{sqrt(169 +360)}}})/(12)
W = (13 +- {{{sqrt(529)}}})/(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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