Question

I am returning to the room is 6 m longer than it is wide and its perimeter is 24 m find the dimension of the room
The length is meters and the width is meters

Answer 1

Let the width of the room be \( w \) meters. Since the length is 6 meters longer than the width, we can express the length as \( l = w + 6 \) meters.

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

\[
P = 2(l + w)
\]

Given that the perimeter is 24 meters, we can set up the equation:

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

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

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

Simplifying this:

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

Dividing both sides by 2:

\[
2w + 6 = 12
\]

Now, subtracting 6 from both sides:

\[
2w = 6
\]

Dividing both sides by 2:

\[
w = 3
\]

Now that we have the width, we can find the length:

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

So the dimensions of the room are:
- Length: 9 meters
- Width: 3 meters

In summary:
- The length is 9 meters.
- The width is 3 meters.