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## finaynay 3 years ago optimization problem: a physical fitness room consists of a rectangular region with a semicircle on each end. if the perimeter of the room is to be a 200 meter running track, find the dimensions that will make the are of the rectangular region as large as possible

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1. geoffb

Do you know how to find the largest area possible?

2. math>philosophy

Draw a picture

3. finaynay

|dw:1353735822700:dw|

4. finaynay

lol

5. math>philosophy

That's fine lol

6. finaynay

c=2piR and 200=4r+2x (x being the base of the rectangle) this is how i set it up

7. math>philosophy

i think you have the perimeter wrong

8. finaynay

how?

9. geoffb

You're not accounting for the circumference of the circle. Your equation only includes the area of the rectangle.

10. geoffb

You would need it to be $$2x + c = 200$$

11. finaynay

c is the circumference right

12. geoffb

Yes, and that's right ($$2 \pi r$$).

13. finaynay

okay and then differentiate that equation correct?

14. geoffb

You would need to differentiate the area, not the perimeter.

15. geoffb

So, can you first determine a formula for the area of your diagram?

16. finaynay

pir^2+2rx

17. geoffb

Yeah, that looks good.

18. finaynay

should i substitute r or x

19. math>philosophy

Whichever one you want

20. finaynay

100/3pi = r seem right?

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