Find the dimensions of a rectangle with area 1000 m^2

Margie Marx 2021-12-16 Answered
Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.
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Expert Answer

lenkiklisg7
Answered 2021-12-17 Author has 29 answers
Let it be: A-area, x width im miles and y-length in miles.
A=xy
We have A=1000, so
1000=xy
y=1000x
Let it be Perimeter - P
P=2x+2y
P=2(x+y)
Substitute y=1000x in equation P=2(x+y)
P=2x+2000x
Compute P(x)
P(x)=22000x2
Find critical points.
22000x2=0
c2=1000
c=1010
Compute P(x):
P(x)=4000x3
P(1010)=400010000010>0
By applying The Second Derivative Test, we have that x=14 is a minimum.
Find y:
We have:
y=10001010
Rationalize:
y=1000101010101010
y=1010
P=4010
Result: x=1010 mis
y=1010 mis
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