Math
April 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!
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
(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
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
Response by poster: 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
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
(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
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
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]
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]
This thread is closed to new comments.
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]