Question

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.)

Answer 1

Answer:

$P(L)=2L+98m^2/L$

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)

$A=L*w$ (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

$w=A/L$ (eq. 3)

$P=2(L+A/L)=2L+2A/L$ (eq. 4)

We know that A=49m^2, plugging in this value into eq. 4, we finally get into the answer:

$P=2L+98m^2/L$

If the length of the rectangle is larger than its width:

$L>w\\L>A/L\\L^2>\sqrt{A} \\|L|>\sqrt{A}$

$|L|>7$

$L<-7 ; L>7$

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