SOLUTION: The length of a rectangle is 1 cm more than 4 times its width. If the area of the rectangle is 72 cm^2, find the dimensions of the rectangle to the nearest thousandth. Thanks

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Question 82346: The length of a rectangle is 1 cm more than 4 times its width. If the area of the rectangle is 72 cm^2, find the dimensions of the rectangle to the nearest thousandth.

Thanks.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let W=width of rectangle
Then length=4W+1
Area(A) of rectangle=Length*Width=W*(4W+1)
Now we are told that:
W*(4W+1)=72 get rid of parens
4W^2+W=72 subtract 72 from both sides
4W^2+W-72=72-72 or
4W^2+W-72=0 quadratic in standard form. We'll use the quadratic formula:
W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
W+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A4%2A%28-72%29+%29%29%2F%282%2A4%29+
W+=+%28-1+%2B-+sqrt%281153%29%29%2F%288%29+
W+=+%28-1+%2Bsqrt+%281153%29%29%2F%288%29+

W+=+4.120 cm ----------------------width of rectangle
4W%2B1=4%284.120%29%2B1=17.480 cm---------------------length of rectangle
Discount negative value for W. Lengths are positive.
CK
A=L*W=(4.120)(17.480)=72 cm^2
~72 cm^2=72 cm^2

Hope this helps----ptaylor