Answer:
[tex]P(x) = 2\left(x+\dfrac{54}{x}\right)[/tex]
Step-by-step explanation:
The area of the rectangle can be written as:
[tex]A = x*h[/tex]
here, x is one side length, and h is the other side length. This area is said to be equal to 54 square meters.
[tex]54 = x*h[/tex]
The perimeter of a rectangle can be written as:
[tex]P = 2x+2h[/tex]
To express perimeter only in terms of x (in other words making it a function P(x)). we need to replace h. And this can be done by using the equation of area that we derived earlier.
[tex]54 = x*h[/tex]
[tex]h=\dfrac{54}{x}[/tex]
now we can substitute this 'h' into our equation of the perimeter.
[tex]P = 2x+2\left(\dfrac{54}{x}\right)[/tex]
[tex]P = 2\left(x+\dfrac{54}{x}\right)[/tex]
and voila! we have expressed P in terms of x only.
this can be written as P as a function of x as:
[tex]P(x) = 2\left(x+\dfrac{54}{x}\right)[/tex]
