Question 85215
Let w=width of rectangle
and l=length of rectangle

Now we are told that 2w+2l, which is the perimeter, equals five times the length

So 2w+2l=5l-------------------------eq1

and 

l*w, which is the area, equals 13.5 sq units, so

l*w=13.5-------------------------------------eq2

substitute w=13.5/l from eq2 into eq1 and we have:

2(13.5/l)+2l=5l  get rid of parens

27/l+2l=5l  multiply each term by l to get rid of the fractions

27+2l^2=5l^2  subtract 2l^2 from both sides

27+2l^2-2l^2=5l^2-2l^2  collect like terms

27=3l^2  divide both sides by 3

l^2=9  take the square root of both sides
l=+or-3 units since lengths are positive we can say that:

l=3 units-------------length 
substitute l=3 into eq1 and we get

2w+2*3=5*3 or
2w+6=15  subtract 6 from both sides

2w+6-6=15-6  collect like terms

2w=9  divide both sides by 2

w=4.5 units--------------------- width

CK
2w+2l=5l
2*(4.5)+2*3=5*3
9+6=15
15=15 

also
l*w=13.5
3*(4.5)=13.5
13.5=13.5


Hope this helps---ptaylor