Posted by **booyah** on Saturday, December 18, 2010 at 7:16pm.

A rectangular dog pen is to be constructed using a barn wall as one side adn 60 meters of fencing for the other three sides. Find the dimensions of the pen that maximize the pen's area.

- Math -
**LULU**, Saturday, December 18, 2010 at 8:00pm
20 x 20

- Math -
**Reiny**, Saturday, December 18, 2010 at 9:49pm
let the length be y m (the single side)

let the width be x m

so we know that 2x + y = 60

or y = 60 - 2x

Area = xy

= x(60-2x)

= -2x^2 + 60x

At this point I don't if you know Calculus or not.

If you do, then

d(Area)/dx = -4x + 60

= 0 for a max of area

-4x + 60 = 0

x = 15

then y = 30

if you don't take Calculus, we have to complete the square

area = -2(x^2 - 30x)

= -2(x^2 - 30x + 225 - 225)

= -2((x-15)^2 - 225)

= -2(x-15)^2 + 450

so the area is a maximum when x = 15

and then y = 60-30 = 30

by either method,

the width has to be 15 m, and the length has to be 30 m for a maximum area of 15(30) or 450 m^2

(LULU's answer only gives an area of 400 )

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