Answer:
width of the room is 3 meters and length is 9 meters
Explanation:
Let's denote the width of the rectangular room as "w" in meters. Since the length is 6 meters longer than the width, the length would be "w + 6" meters.
The perimeter of a rectangle is the sum of the lengths of all four sides. In this case, the perimeter is given as 24 meters:
Perimeter = 2 * Length + 2 * Width
Substituting the length and width with their expressions in terms of "w", we get:
24 = 2 * (w + 6) + 2 * w
Simplifying the equation, we can distribute the 2 and get:
24 = 2w + 12 + 2w
Combining like terms, we can simplify the equation to:
24 = 4w + 12
Subtracting 12 from both sides, we get:
12 = 4w
Dividing both sides by 4, we get:
w = 3
So the width of the room is 3 meters.
Using the expression for the length, we can find the length of the room:
Length = w + 6 = 3 + 6 = 9 meters
So the dimensions of the room are 9 meters by 3 meters.