SOLUTION: The length of a rectangle is 5 cm more than 4 times its width. If the area of the rectangle is 80 cm2, find the dimensions of the rectangle to the nearest thousandth. Please

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Question 95455: The length of a rectangle is 5 cm more than 4 times its width. If the area of the rectangle is 80 cm2, find the dimensions of the rectangle to the nearest thousandth.

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Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=width
Then length (l)=4w+5 (we are told this)
Area of a rectangle =length x width. So we have
80=w(4w+5) get rid of parens
80=4w^2+5w subtract 80 from both sides
4w^2+5w-80=80-80 or
4w^2+5w-80=0---------quadratic in standard form
Solve using the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A4%2A%28-80%29+%29%29%2F%282%2A4%29+
x+=+%28-5+%2B-+sqrt%281305%29%29%2F%288%29
x+=+%28-5+%2B-+36.125%29%2F%288%29
Disregard the negative value for x. Lengths and widths are positive
x+=+%28-5+%2B36.125%29%2F%288%29
x+=+31.125%2F%288%29
x+=+3.891cm--------------------width
4x%2B5=4%283.891%29%2B5+=+20.562cm-------------length
CK
A=l%2Aw=3.891%2A20.562=80.008 cm
~80=~80
Hope this helps---ptaylor