What is the minimum length of fencing required for a rectangular enclosure with an area of 72m^2 and one side of the enclosure does not need fencing?

Answer 1

Rosario

Suppose one side of the rectangle is y and the other two (opposite) sides are x

Then xy = 72 as that is the area and we want to minimise

L = 2x + y (length of fence)

L = 2x + (72/x)

dL/dx = 2 - (72/x²)

To minimise L we need dL/dx = 0, ie 2 - (72/x²) = 0 or 2x² = 72, x² = 36, so x = 6.

x = 6, y = 12, so minimum length of fence needed = 12 + 6 + 6 = 24 m

Mike