Question

A farmer decides to build a fence to enclose a rectangular field in which he will plant a crop he has 1000 feet of fence to use and his goal is to maximize the area of the field. One side must be 200 feet

Answer 1

Answer:

Length of the other side will be 300 feet.

Step-by-step explanation:

Given:

Length of the fence he has = 1000 feet.

One side = 200 feet;

we need to find the other side.

Solution:

Let the other side be denoted by 'x'.

Now given that;

Farmer has 1000 feet of fencing used to fence the rectangular field.

So we can say that;

Perimeter of the field = 1000 feet.

Now we know that;

Perimeter is equal to twice the sum of two sides of the rectangle.

framing in equation form we get;

$1000=2(200+x)$

Applying Distributive property we get;

$1000=400+2x$

Subtracting both side by 400 we get;

$1000-400=400+2x-400\\\\2x=600$

Now Dividing both side by 2 we get;

$\frac{2x}{2}=\frac{600}{2}\\\\x=300\ ft$

Hence Length of the other side will be 300 feet.