A rectangle has area 16 m^2 . Express the perimeter of the rectangle as a function of the length of one of its sides

General
1

A rectangle has area 16 m^2 . Express the perimeter of the rectangle as a function of the length of one of its sides.

2

A rectangle has area 16 m². Express the perimeter of the rectangle as a function of the length of one of its sides.

Answer: To express the perimeter of the rectangle as a function of the length of one of its sides, let’s denote the length of one side as ( l ) (in meters). Given that the area of the rectangle is 16 m², we can find the other side’s length in terms of ( l ).

Step-by-Step Solution:

  1. Area of the Rectangle:
    The area ( A ) of a rectangle is given by the product of its length ( l ) and width ( w ):

    A = l \times w

    Given that the area ( A ) is 16 m²:

    l \times w = 16

  2. Express Width in Terms of Length:
    Solving for ( w ) in terms of ( l ):

    w = \frac{16}{l}

  3. Perimeter of the Rectangle:
    The perimeter ( P ) of a rectangle is given by the sum of all its sides:

    P = 2l + 2w

    Substitute ( w ) with ( \frac{16}{l} ):

    P = 2l + 2\left(\frac{16}{l}\right)

    Simplify the expression:

    P = 2l + \frac{32}{l}

Final Function:

The perimeter ( P ) of the rectangle as a function of the length ( l ) of one of its sides is:

P(l) = 2l + \frac{32}{l}

This function ( P(l) ) gives the perimeter of the rectangle for any given length ( l ) of one side, provided ( l ) is a positive real number.