A rectangular garden pond is being designed to have a water area of 6 m2.?

| September 4, 2012 | 0 Comments

Question by mojo jojo: A rectangular garden pond is being designed to have a water area of 6 m2.?
A rectangular garden pond is being designed to have a water area of 6 m2. 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.

Best answer:

Answer by fabianfucci
A = water area = x * y
B = margin of flower bed in one direction
C = margin of flower bed in the other direction

Total area = 2 * B * x + 2 * C * y + x * y + 4 * B * C

Total area is a function of x and y, and it is a surface in 3D space. Find the derivatives of the total area and make them equal to zero. Solve for x and y.

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