Question

Find the dimensions of a rectangle with area 343000 m2 whose perimeter is as small as possible.

Answer 1

LB = 343,000

B = 343,000 / L

minimizing perimeter is same as minimizing semi-perimeter S
S = L + B = L + 343,000 / L

S' = 1 - 343,000 /L^2

setting S' to zero & taking the +ve value,

L = sqrt(343,000) = 585.66 m

since a rectangle with integer sides is wanted,

dimensions = 585 m x 586 m
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