# Find the dimensions of a rectangle with area 1,000 m2 whose perimeter is as small as possible.?

• Find the dimensions of a rectangle with area 1,000 m2 whose perimeter is as small as possible.?

Answer #1 | 24/04 2017 21:39
the rectangle with the smallest perimeter is a square. thus, the dimensions of all four sides are sqrt(1000) or 10 * sqrt(10) ==> 31.6 feet more or less
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Answer #2 | 24/04 2017 21:46
Let l, w represent the length and width of rectangle, respectively Area = lw = 1000 so l = 1000/w Perimeter is P(l, w) = 2l + 2w = 2(1000/w) + 2w The minimum of P(w) is identified by solving dP/dw = 0 That's -2000/w² + 2 = 0 Solve for w, then compute l and P(l, w) to complete the exercise Can you take it from here so you can tell your instructor that YOU “completed” the exercise? If not, GL! I would give you the final answer to your question, but then you would have to split the credit with me. I am sure one of my Y!A colleagues will supply you with the specific answer to this exercise. But that will not help you next time, and THERE WILL BE A NEXT TIME!
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