Question 85215: if the area of a rectangle is 13.5 square units and the length is 1/5 the perimeter. what is the length and width of the rectangle?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! 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
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