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wlad13 [49]
3 years ago
10

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

Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0
LB = 343,000 

<span>B = 343,000 / L </span>

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

<span>S' = 1 - 343,000 /L^2 </span>

<span>setting S' to zero & taking the +ve value, </span>

<span>L = sqrt(343,000) = 585.66 m </span>

<span>since a rectangle with integer sides is wanted, </span>

<span>dimensions = 585 m x 586 m </span>
<span>------------------- --------------------</span>
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