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

Answer:

$P(x) = 2\left(x+\dfrac{54}{x}\right)$

Step-by-step 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.

$54 = x*h$

$h=\dfrac{54}{x}$

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

$P = 2x+2\left(\dfrac{54}{x}\right)$

$P = 2\left(x+\dfrac{54}{x}\right)$

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

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

$P(x) = 2\left(x+\dfrac{54}{x}\right)$