Using a system of equations, it is found that for the room's dimensions:
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]
A similar problem is given at https://brainly.com/question/9553406