Question

Suppose that a rectangle has an area of 54 square meters. Express the perimeter P as a function of the length x of one of the sides.

Answer 1

`P(x) = 2\left(x+(54)/(x)\right)`

Explanation:

The area of the rectangle can be written as:

`A = x*h`

here, x is one side length, and h is the other side length. This area is said to be equal to 54 square meters.

`54 = x*h`

The perimeter of a rectangle can be written as:

`P = 2x+2h`

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.

`54 = x*h`

`h=(54)/(x)`

now we can substitute this 'h' into our equation of the perimeter.

`P = 2x+2\left((54)/(x)\right)`

`P = 2\left(x+(54)/(x)\right)`

and voila! we have expressed P in terms of x only.

this can be written as P as a function of x as:

`P(x) = 2\left(x+(54)/(x)\right)`