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| Math Central | Quandaries & Queries |
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Question from Mark, a student: a rectangular field is to be enclosed and divided into four equal lots by fences parallel to one of the side. A total of 10000 meters of fence are available .Find the area of the largest field that can be enclosed. |
Hi Mark,
Draw a diagram!
The measurements are in metres.
All together you need five lengths of length y meres each and two lengths of length x metres each. You have 10 000 metres of fencing so
5y + 2x = 10 000.
The area A is given by
A = xy square metres.
Solve the first equation for y and substitute into the second equation. Use the calculus you know to find the value of x that maximizes the area.
Penny
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