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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