I can't understand the textbook answer of the length equal to 190 m approximately and the width equal to 63 m in the following problem.An animal...

The breeder has to construct 5 rectangular pens which are
adjacent to each other. Let the sides of the pens have lengths S1 and S2 and let the
common side S2.

The length of fence required to construct
this is 10*S1 + 6*S2

The area of each pen is 2400
m^2

=> S1*S2 =
2400

=> S1 =
2400/S2

The length of fence can be rewritten as : 24000/S2
+ 6*S2

The length has to be minimized. This is done by
finding the derivative and solving it for s

-24000/S2^22 +
6 = 0

=> S2^2 = 24000/6 =
4000

=> S2 = sqrt 4000 = 63.52
m

S1 = 2400/S2 = 37.78

For
each pen the length is 63.52 m  and the width is 37.78 m. Multiplying 37.78 by 5 gives
approximately 180 m. So the dimensions in your book are the width of each pen and the
length made up by adding the shorter side of each
pen.

To minimize the length of the fence
required the length of each pen should be 63.52 m and the width of
each pen should be 37.78 m.