## anonymous one year ago Rectangle R has varying length L and width W but with a constant area of 4 square feet. a)Express the perimeter P as a function of length L. What type of function is P? What is the domain of P? (I only help with parts B and C) b)Describe the asymptotic behavior of P. What can you say about rectangle R because of this behavior? c) For what values of L and W will the perimeter of R be the least? Give a geometric explanation.

1. anonymous

I only help with parts B and C

2. ganeshie8

what do you have for part A ?

3. ganeshie8

i ask because PartB and C depend on part A

4. triciaal

|dw:1436241409178:dw|

5. anonymous

I have P = 2(4+L^2)/L

6. triciaal

@mahima2558 do you have the same for part A?

7. triciaal

|dw:1436242085909:dw|

8. ganeshie8

\[\large P = \dfrac{2(4+L^2)}{L}\] looks good

9. anonymous

so for part b, is L=0 the only asymptote

10. anonymous

and I'm not sure what I can say about the rectangle from that

11. ganeshie8

Look at the graph of P |dw:1436239083007:dw|

12. ganeshie8

x axis is L y axis is P

13. ganeshie8

what do you notice in the graph as you increase L ?

14. anonymous

P increases?

15. ganeshie8

Yes, what happens if you increase L too much

16. ganeshie8

P also increases and the rectangle looks as if it is a thin line, yes ? |dw:1436239328327:dw|

17. anonymous

yes

18. ganeshie8

just explain that in ur own words for part b

19. ganeshie8

also explain what happens to P and how the rectangle looks as you make L very low

20. anonymous

ok that makes sense

21. anonymous

for part c do i use the graph to find the value of L and W were P would be the least?

22. ganeshie8

that will do!

23. anonymous

the minimum value of the graph is (2,8) so that means the length is 2 and the perimeter is 8

24. anonymous

so the width would be 2 as well?

25. anonymous

ok great, thank you

26. ganeshie8

yw!