Word Problems - Distance between 2 objects, maximizing area, and more

**xkncx** · February 27th 2008, 06:54 AM

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

**Peritus** · February 27th 2008, 07:15 AM

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:

$\begin{gathered} 2\left( {a + b} \right) = 25 \hfill \\ S = ab = a\left( {\frac{{25}} {2} - a} \right) \hfill \\ \end{gathered}$

now let's differentiate S(a):

$\frac{{dS}} {{da}} = \frac{{25}} {2} - 2a = 0 \Rightarrow a = \frac{{25}} {4},b = \frac{{25}} {4}$

you can differentiate S one more time to make sure that it's maxima.