Respuesta :

Using a system of equations, it is found that for the room's dimensions:

  • The width is of 32.33 feet.
  • The length is of 66.67 feet.

The perimeter of a rectangle of length l and width w is given by:

[tex]P = 2(l + w)[/tex]

The length of a rectangular room is 2 feet longer than twice the width, hence:

[tex]l = 2w + 2[/tex]

The room's perimeter is 196 feet, hence:

[tex]2l + 2w = 196[/tex]

From the second equation:

[tex]2(2w + 2) + 2w = 196[/tex]

[tex]6w = 194[/tex]

[tex]w = \frac{194}{6}[/tex]

[tex]w = 32.33[/tex]

Then:

[tex]l = 2w + 2 = 2(32.333) + 2 = 66.67[/tex]

  • The width is of 32.33 feet.
  • The length is of 66.67 feet.

A similar problem is given at https://brainly.com/question/9553406