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antiseptic1488 [7]
4 years ago
7

A farmer wants to make a rectangular field with a total area of 3200 m2. It is surrounded by a fence. It is divided into 3 equal

areas by fences. What is the shortest total length of fence with which this can be done? meters
Mathematics
1 answer:
Sloan [31]4 years ago
5 0

Answer:

The shortest total length of fence with which this can be done is 40m^2

Step-by-step explanation:

Lets say that your area has width   w    and length l.    Since you want to divided it into 3 equal areas by fences there would be 4  lengths and the area and perimeter would be given by the following equations.

3200 =  w*l

Perimeter = P =  4l+2w = 4l + \frac{2*3200}{l}

We want to optimize the perimeter so

P'(l) = 4-\frac{6400}{l^2} = 0

Solving for  l    we get

l = 40.

Since   3200 =  l*w    and   l = 40    then    w = 3200/40  = 80

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It’s a little complicated but here’s how it works:
Imagine a table with the intervals
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A radio station broadcasts a signal over qn area with a radius of 50 miles. The station can relay the signal and broadcast over
denpristay [2]
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</span>
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