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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

ou would have 12 of each