Any help will be greatly appreciated

An envelope is 4cm longer then it is wide. The area is 96 sq. cm Find the length and width. Use a polynomial equation.

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- Mar 25th 2008, 09:49 AMimbadatmathusing a polynomial equation
Any help will be greatly appreciated

An envelope is 4cm longer then it is wide. The area is 96 sq. cm Find the length and width. Use a polynomial equation. - Mar 25th 2008, 09:57 AMPeritus
$\displaystyle

\begin{gathered}

S_{envelope} = w(w + 4) = 96 \hfill \\

w^2 + 4w - 96 = 0 \hfill \\

\end{gathered} $

solve the quadratic equation to obtain the solution - Mar 25th 2008, 10:32 AMimbadatmath
am i doing this correctly?

w-12=0

+12 +12

w=12

w+8=0

-8 -8

w=-8 - Mar 25th 2008, 10:50 AMmathceleb
- Mar 25th 2008, 11:27 AMimbadatmath
would it be

12(12+4)=96 - Mar 25th 2008, 11:40 AMiknowone
12*(12+4)= 12*16 =192 so that's cant be right.

the factoring of your polynomial should be (x-8)(x+12) which gives you x-8 = 0 or x+12 = 0, meaning x=8 or x=-12. Since x is a length and cant be negative the answer must be x=8.

Does it work?

8*(4+8) = 8*12 = 96! - Mar 25th 2008, 11:48 AMimbadatmath
so what i was doing before

w-12=0

+12 +12

w=12

w+8=0

-8 -8

w=-8

was going in the total wronge direction? - Mar 25th 2008, 01:08 PMiknowone
No, it is just that your signs were backwards.

(w-8)(w+12) = w^2 + 4w - 96

where as

(w+8)(w-12) = w^2 - 4w - 96

Notice that the first quadratic equation is the one you are working with. The second equation above is similar to the first but the middle w-term is negative when it should be positive.