SOLUTION: A rectangular garden is to be fenced using the wall of a house as one side of the garden.the garden should have an area of 40mē. Determine the minimum perimeter and dimensions

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Question 1079544: A rectangular garden is to be fenced using the wall of a house as one side of the
garden.the garden should have an area of 40mē. Determine the minimum perimeter and dimensions of the garden
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the side parallelto the house = +y+
Let each of the other 2 sides = +x+
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Equation for area:
+x%2Ay+=+40+ m2
+y+=+40%2Fx+
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Let +P+ = the perimeter of the 3 walls
+P+=+40%2Fx+%2B+2x+
First I'll show a plot of +P+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-3%2C+30%2C+40%2Fx+%2B+2x+%29+
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Assuming this is a calculus problem,
I'll find the derivative:
+Q+=+-40%2Fx%5E2+%2B+2+
Find where the slope = 0
+-40%2Fx%5E2+%2B+2+=+0+
+40%2Fx%5E2+=+2+
+2x%5E2+=+40+
+x%5E2+=+20+
+x+=+4.472+
and
+y+=+40%2Fx+
+y+=+40%2F4.472+
+y+=+8.944+
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The dimensions are 4.472 x 8.944
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The minimum perimeter is:
+P+=+40%2Fx+%2B+2x+
+P+=+8.944+%2B+8.944+
+P%5Bmin%5D+=+17.89+ m
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check the math & possibly get another opinion