The length of a rectangle is 3cm more than 2 times its width. If the area of the rectangle is 99cm^2, what are the dimensions of the rectangle to the nearest thousandth???
Is it set up like this .....
L = 3 + 2w
I am lost on what to do after that !
2007-02-04 15:23:04 · 4 answers · asked by CookFrNW 3 in Science & Mathematics ➔ Mathematics
l=2w+3
A=99=lw substitute 2w+3 for l
99=w(2w+3)
99=2w^2+3w subtract 99 from each side
2w^2+3w-99=0
w=(-3+/-√(9+8*99))/4
w=3/4+/-.25√(801)
w=-.75+/-.75√89
since w>0
w=.75(-1+√89)=6.325 cm
l=2w+3=15.651 cm
2007-02-04 15:38:24 · answer #1 · answered by yupchagee 7 · 15⤊ 0⤋
equation 1: L x W = 99cm^2
equation 2: L = 3cm + 2w
Solve for L and W for Length and Width:
Solve by substitution into equation1:
(3cm + 2w) x w = 99cm^2
>> 2w^2 + 3w = 99cm^2
>> 2w^2 +3w -99cm^2 = 0
using the quadratic formula we can solve this quadratic equation:
(-3 +- sqrt(801)) / 4
>>(-3 +- 28.30194 )/4
we get 2 answers:
w = 6.3254 and -7.8254
We will choose the positive answer because you cannot have a negative width in real life.
Now moving along to solve the rest of the problem:
L x 6.3254cm = 99cm^2
L = 99cm^2 / 6.3254cm
L= 15.651
Conclusion:
The dimensions of the rectangle are:
Length= 15.651 cm
Width = 6.325 cm
2007-02-04 23:48:46 · answer #2 · answered by Plabomano 1 · 0⤊ 0⤋
L=2w+3 is correct.
The area is 99cm^2 and are of a rectangle is length times width, so A=LW
or 99cm^2=W(2w+3)
99cm^2=2w^2+3W
set it equal to zero.
2w^2+3w-99=0
Next use the quadriatic formula to solve for w and then substitute w into L=2w+3 to get the dimensions of the recangle.
2007-02-04 23:29:25 · answer #3 · answered by Woot 3 · 0⤊ 0⤋
99cm^2 = LxW
Plug in L in terms of W
99cm^2= (3+2W)W
and solve for W
then plug in your value for W and solve for L
2007-02-04 23:26:43 · answer #4 · answered by Anonymous · 0⤊ 0⤋