ANSWER:
length: 56ft
width: 26ft
STEP-BY-STEP EXPLANATION:
Given:
width = w
length = 4 + 2w
The perimeter is the sum of all the sides of the rectangle, therefore:
[tex]\begin{gathered} w+l+w+l=164 \\ 2w+2l=164 \\ \text{ we replacing and solving for w:} \\ 2w+2\cdot(4+2w)=164 \\ 2w+8+4w=164 \\ 6w=164-8 \\ w=\frac{156}{6} \\ w=26\text{ ft} \end{gathered}[/tex]Now, since the length is a function of the width, we can calculate it like this:
[tex]\begin{gathered} l=4+2\cdot26 \\ l=4+52 \\ l=56\text{ ft} \end{gathered}[/tex]Therefore, the dimensions of the room are 26 feet wide and 56 feet long.
