Find the minimum length of fence needed for a play area with area 60.5 m2. What are the dimensions of the play area?

The answer is below

Step-by-step explanation:

Let x and y represent the length and the width of the play area. Hence:

xy = 60.5

y = 60.5 / x

The perimeter (P) of the play area is given as:

P = 2(x + y)

substitute for y:

P = 2(x + 60.5/x)

P = 2x + 121/x

The minimum area is at P' = 0. Hence:

P' = 2 - 121/x²

0 = 2 - 121 / x²

121 / x² = 2

x² = 60.5

x = √60.5

Also, y = 60.5 / x = 60.5 / √60.5

y = √60.5

Therefore the minimum perimeter is:

P = 2(√60.5 + √60.5) = 31.11 m