Question

A rectangular room is 6 meters longer than it is wide,
and its perimeter is 32
meters. Find the dimensions of the room.

The length is :
meters and the width is
meters.

Answer 1

Let the width of the room be \( w \) meters. According to the problem, the length \( l \) can be expressed as:

\[
l = w + 6
\]

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

\[
P = 2l + 2w
\]

We know the perimeter is 32 meters, so we can set up the equation:

\[
2(w + 6) + 2w = 32
\]

Now, simplify this equation:

\[
2w + 12 + 2w = 32
\]
\[
4w + 12 = 32
\]
Subtract 12 from both sides:

\[
4w = 20
\]
Dividing both sides by 4:

\[
w = 5
\]

Now, use this value to find the length:

\[
l = w + 6 = 5 + 6 = 11
\]

Thus, the dimensions of the room are:
- Length: 11 meters
- Width: 5 meters

To summarize:
- The length is **11 meters** and the width is **5 meters**.