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?

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.

Question

Mathematics

Alivia

14 April, 21:46

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?

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.

+4

Answers (1)

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Hubby · Answer 1

A is area & constant

A=4

wL=A; perimeter is p; p = 2w + 2L

w = A/L allows for p=2 x (multiplication) (A/L) + 2L

Domain for p is L>0

Knowing that A=4, p=2 x (multiplication) (A/L) + 2L

p = 8/L + 2L