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nevsk [136]
3 years ago
5

Find a formula for the described function. A rectangle has area 49 m2. Express the perimeter of the rectangle as a function of t

he 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.)
Mathematics
1 answer:
Anna71 [15]3 years ago
7 0

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 <em>w </em>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

L7

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

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