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# MathApril 13, 2009 4:59 PM   Subscribe

A rectangle has an area of 5.7. its length is 2.3 feet longer than its width, what are the dimensions? Thanks everyone!
posted by Benzle to science & nature (9 answers total) 1 user marked this as a favorite

A = W*L;
L = W+2.3;
A = W*(W+2.3);
5.7 = W*(W+2.3)

Does this make sense to you? Can you take it from there? Also, is this homework?
posted by telegraph at 5:01 PM on April 13, 2009 [1 favorite]

Great, thanks so much,
posted by Benzle at 5:03 PM on April 13, 2009

Area of triangle= (Length*Width)/2

(2.3x*x)/2=5.7

x=2.2263

So width=2.2263 and length=5.1205

posted by Chan at 5:04 PM on April 13, 2009

L x W = 5.7

L = W + 2.3

W(W + 2.3) = 5.7

W^2 + 2.3W = 5.7

W^2 + 2.3W - 5.7 = 0

W = 1.5
L = 1.5 + 2.3 = 3.8
posted by bowmaniac at 5:04 PM on April 13, 2009

bowmaniac,

how do you get from step,

W^2 + 2.3W - 5.7 = 0

to,

W = 1.5

When I try this in the quadratic formula I get a negative sqr. root

I.E.
(-2.3 +- sqrrt.(2.3^2 -4(-5.7))/2
posted by Benzle at 5:08 PM on April 13, 2009

You've got a positive square root there, you're just missing the double negative:
(2.32 - 4 (-5.7))/2)
posted by Lemurrhea at 5:12 PM on April 13, 2009

I cheated and used http://www.math.com/students/calculators/source/quadratic.htm
a = 1
b = 2.3
c = -5.7
posted by bowmaniac at 5:13 PM on April 13, 2009

Benzle -- note that the "+-" in the quadratic formula is an either/or -- there are two solutions, one using plus and the other using minus. At least one of these is positive in this situation.
posted by telegraph at 5:14 PM on April 13, 2009

OK, based on your previous "Help-me-open-a-curry-restaurant-franchise-Filter" question, I'm going to assume this is not your homework. So:

Let the length and width be "L" and "W". Then:

L = W + 2.3

The area of a rectangle is the product of its length and width, so:

L * W = 5.7

that assumes that the area is 5.7 square feet; you didn't specify the unit of the area, and the question is unanswerable without it. anyway...

Put those two equations together, and:

(W + 2.3) * W = 5.7

W^2 + 2.3 * W = 5.7

W^2 + 2.3 * W - 5.7 = 0

Plug that into the quadratic formula:

W = (-2.3 +/- sqrt(2.3^2 - 4 * 1 * (-5.7)) / (2 * 1)

W = (-2.3 +/- sqrt(5.29 + 22.8)) / 2

W = (-2.3 +/- sqrt(28.09)) / 2

W = (-2.3 +/- 5.3) / 2

Clearly the width is not negative, so we can throw away the "or minus" of that "plus or minus", and so:

W = (-2.3 + 5.3) / 2

W = 3 / 2

W = 1.5

And since L = W + 2.3:

L = 1.5 + 2.3

L = 3.8

So, the length is 3.8 and the width is 1.5. Double checking that these numbers fit the original equations:

L = W + 2.3

3.8 = 1.5 + 2.3

3.8 = 3.8 (correct)

L * W = 5.7

3.8 * 1.5 = 5.7

5.7 = 5.7 (correct)
posted by Flunkie at 5:19 PM on April 13, 2009 [2 favorites]

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