Question

A rectangular room is 6 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of. the room.

The length is : _____ meters and the width is _____ meters.​

Answer 1

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.