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Vladimir79 [104]
3 years ago
7

A rectangular garden 200 square feet in area is to be fenced o against rabbits. Find thedimensions that will require the least a

mount of fencing given that one side of the garden isalready protected by a barn
Mathematics
1 answer:
Rudiy273 years ago
8 0

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

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