Final answer:
The dimensions of the rectangular room, where it is 3 meters longer than it is wide and has a perimeter of 26 meters, are a length of 8 meters and a width of 5 meters.
Step-by-step explanation:
To find the dimensions of the rectangular room where the room is 3 meters longer than it is wide and its perimeter is 26 meters, we can let the width be w meters. Therefore, the length will be w + 3 meters. The perimeter of a rectangle is calculated as 2 × (length + width), which in this case is 2 × (w + w + 3) = 26 meters.
Combining like terms, we get 2 × (2w + 3) = 26 → 4w + 6 = 26. Subtracting 6 from both sides gives us 4w = 20, and dividing by 4 gives us w = 5. Therefore, the width is 5 meters and the length is 5 + 3 = 8 meters.
The dimensions of the room are a length of 8 meters and a width of 5 meters.