I just need help on questions 7, 8, 9, 12, and 13
For question 7, I keep thinking that the pool area is a square, so wouldn't all sides be equally fenced? Therefore wouldn't the 25M be equally divided by 4 to maximize area?
Thank-you in advance
I just need help on questions 7, 8, 9, 12, and 13
For question 7, I keep thinking that the pool area is a square, so wouldn't all sides be equally fenced? Therefore wouldn't the 25M be equally divided by 4 to maximize area?
Thank-you in advance
7. square is just a special case of rectangle whose adjacent sides are equal.
let's denote one of the sides as a and the other as b thus:
$\displaystyle \begin{gathered}
2\left( {a + b} \right) = 25 \hfill \\
S = ab = a\left( {\frac{{25}}
{2} - a} \right) \hfill \\
\end{gathered} $
now let's differentiate S(a):
$\displaystyle \frac{{dS}}
{{da}} = \frac{{25}}
{2} - 2a = 0 \Rightarrow a = \frac{{25}}
{4},b = \frac{{25}}
{4}$
you can differentiate S one more time to make sure that it's maxima.