word problem: The length of a rectangle is 3 cm more than 2

Algebra and word problems. I can't seem to get the right answer.

The length of a rectangle is 3 cm more than 2 times its width. If the area of the rectangle is 99 cm2, find the dimensions of the rectangle to the nearest thousandth.

This is what I did:

Let the length be denoted by "L" and the width be denoted by "w". Then the equations are:

L = 2w + 3

L - 2w = 3………(1)

Lw = 99…………………(2)

From (2) I get:

w=99/L

Substituting this in (1) I get:

L - 2(99/L) = 3

Multiplying throughout by L I get:

L^2 - 198 = 3L
L^2 - 3L - 198 = 0
L = [3+/-sqrt(9 + 792)]/21 = 3+/-sqrt(801)/21 = 3 + 28.3/21 = 15.65

Is this right?
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Edited by stapel -- Reason for edit: formatting

the equations arel=2w+3=>l-2w=3………(1)lw=99…………………..(2)from (2) w=99/lsubstituting this in (1)l-2(99/l)=3multiplying throughout by ll^2-198=3l=>l^2-3l-198=0=>l=[3+/-sqrt(9+792)]/21=3+/-sqrt(801)/21=3+28.3/21=15.65

Please DO NOT post in that fashion: IMPOSSIBLE to follow; rearrange:

the equations are
l = 2w + 3
l - 2w = 3………(1)
lw = 99..……….(2)
from (2): w = 99 / l
substituting this in (1): l - 2(99 / l) = 3
multiplying throughout by l: l^2 - 198 = 3l
l^2 - 3l - 198 = 0
l = [3 +/- sqrt(9 + 792)] / 21 : WHERE DOES 21 COME FROM?
l = 3 +/- sqrt(801) / 21 : WHY DID YOU DROP THE BRACKETS?
l = 3 + 28.3 / 21 = 15.65 : HOW DID YOU GET 15.65 FROM THAT?

AND NEVER use l as a variable: looks too much like 1 !

Can you follow this:
Let w = width: then length = 2w + 3

area = width times length = w(2w + 3)
since area = 99 then:
w(2w + 3) = 99
2w^2 + 3w - 99 = 0

Now solve that for w; OK?

still confused

how did yours turn out to be so much shorter? I still can't figure out how this is going to work.
w(2w + 3) = 99
2w^2 + 3w - 99 = 0

because there is no number I can think of that will stand as w to get 99.

We can use the quadratic formula:\(\displaystyle \L \;w = \frac{{ - b \pm sqrt{b^2 - 4ac}}}{{2a}}\)

Quadratics are in the form:

\(\displaystyle \L \;ax^2\,+\,bx\,+\,c\,=0\)

\(\displaystyle \L \;2w^2\,+\,3w\,-\,99\,=\,0\)


Identify your \(\displaystyle a\), \(\displaystyle b\), and \(\displaystyle c\). As Stapel said, plug and chug!