Question

A rectangular shed covers 800 square feet of ground. It is 10 feet longer than it is wide.
What is the width of the shed to the nearest tenth of a foot?

Answer 1

So \(A =lw\)\[\begin{align}
A = w \cdot (10+w)
\\&: ~A = 10w +w^2
\\&: ~800 = 10w+w^2
\\&: ~w^2+10w-800=0
\end{align}\]First check to see if the discriminant of this quadratic is positive. If it is, then you can state that you have 2 solutions.
\[\begin{align}
b^2-4ac = (10)^2 -4(1)(-800) = 3300
\end{align}\]This means you have 2 solutions.

Answer 2

one of the solutions is negative, so you can reject it

Answer 3

\[\begin{align}\
w^2+10w-800=0
\\&: (w^2+10w)-800=0
\\&: (w^2+10w+25\color{red}{-25})-800\color{red}{-25}=0
\\&: (w+5)^2 -825=0
\\&: (w+5)^2 = 825
\\&: w+5 = \pm\sqrt{825}
\\&: w = -5 \pm \sqrt{825}
\end{align}\]

Answer 4

So tell me which value of w is positive :)