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Dimensions of the garden to minimize the total area?

A rectangular garden pond is being designed to have a water area of 6 m^2. Around the edge there will be a flower bed for water loving plants, 0.5 m wide on two opposite sides and 1 m wide on the other two opposite sides. Find the dimensions of the garden to minimize the total area of the pond and flower bed.

Public Comments

1. 1m x.5m and 3m deep.
2. Let the dimensions of the pond be x and y. Then xy = 6 and the area of the flower beds A = x + 2y = x + 12/x = x + 12x^(-1) dA/dx = 1 - 12x^(-2) dA/dx when 12x^(-2) = 1 x^(-2) = 1/12 x = sqrt(12), y = sqrt(3) so the garden dimensions are 1 + sqrt(12) and 2 + sqrt(3)