## finaynay Group Title 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 one year ago one year ago

1. geoffb Group Title

Do you know how to find the largest area possible?

2. math>philosophy Group Title

Draw a picture

3. finaynay Group Title

|dw:1353735822700:dw|

4. finaynay Group Title

lol

5. math>philosophy Group Title

That's fine lol

6. finaynay Group Title

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

7. math>philosophy Group Title

i think you have the perimeter wrong

8. finaynay Group Title

how?

9. geoffb Group Title

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

10. geoffb Group Title

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

11. finaynay Group Title

c is the circumference right

12. geoffb Group Title

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

13. finaynay Group Title

okay and then differentiate that equation correct?

14. geoffb Group Title

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

15. geoffb Group Title

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

16. finaynay Group Title

pir^2+2rx

17. geoffb Group Title

Yeah, that looks good.

18. finaynay Group Title

should i substitute r or x

19. math>philosophy Group Title

Whichever one you want

20. finaynay Group Title

100/3pi = r seem right?