Find a formula for the described function. A rectangle has area 49 m2. Express the perimeter of the rectangle as a function of the length L of one of its sides. P(L) = ___State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval notation.)

Accepted Solution

Answer:[tex]P(L)=2L+98m^2/L[/tex]Step-by-step explanation:The area (A) of a rectangle is equal to the length (L) of one of its sides times its width (w)[tex]A=L*w[/tex] (eq. 1)And its perimeter can be calculated with the next formula:P=2(L+w) (eq. 2)Solving for w in eq. 1, and plugging it into eq. 2[tex]w=A/L[/tex] (eq. 3)[tex]P=2(L+A/L)=2L+2A/L[/tex] (eq. 4)We know that A=49m^2, plugging in this value into eq. 4, we finally get into the answer:[tex]P=2L+98m^2/L[/tex]If the length of the rectangle is larger than its width:[tex]L>w\\L>A/L\\L^2>\sqrt{A} \\|L|>\sqrt{A}[/tex][tex]|L|>7[/tex][tex]L<-7 ; L>7[/tex]We know that a length can't be negative value, so the only valid interval is L>7. The domine of P is then:L>7