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

Let's denote the width of the room as \( w \) meters. According to the problem, the length \( l \) of the room is \( w + 6 \) meters.

The formula for the perimeter \( P \) of a rectangle is given by:

\[
P = 2l + 2w
\]

We know the perimeter is 24 meters, so we can set up the equation:

\[
2l + 2w = 24
\]

Substituting \( l \) with \( w + 6 \):

\[
2(w + 6) + 2w = 24
\]

Expanding the equation:

\[
2w + 12 + 2w = 24
\]

Combining like terms:

\[
4w + 12 = 24
\]

Now, subtract 12 from both sides:

\[
4w = 12
\]

Dividing by 4:

\[
w = 3
\]

Now, we can find the length:

\[
l = w + 6 = 3 + 6 = 9
\]

So, the dimensions of the room are:

- Width: \( 3 \) meters
- Length: \( 9 \) meters

**Final dimensions:**
- Length: \( 9 \) meters
- Width: \( 3 \) meters