Question

A rectangular garden 200 square feet in area is to be fenced o against rabbits. Find thedimensions that will require the least amount of fencing given that one side of the garden isalready protected by a barn

Answer 1

Answer:

20 ft by 10ft

Step-by-step explanation:

Area of the garden =200 square feet

Let the dimensions of the garden be x and y

Area, xy=200

$x=\frac{200}{y}$

Since one side is already protected by a barn,

Perimeter of the garden=2x+y

$P(y)=\frac{2X200}{y}+y$

$P(y)=\frac{400}{y}+y$

$P(y)=\frac{400+y^2}{y}$

The minimum point of P(y) is the point where its derivative equals zero.

$P^{1}(y)=\frac{y^2-400}{y^2}$

$\frac{y^2-400}{y^2}=0$

$y^2-400=0$

$y^2=400$

y=20feet

Recall:

xy=200

20x=200

x=10feet

The dimensions of the garden that will require minimum fencing is 20 ft by 10ft