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

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Question 1045783: A rectangular room is 6 meters longer than it is wide, and its perimeter is
24 meters. Find the dimension of the room.

Found 3 solutions by ikleyn, josgarithmetic, josmiceli:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A rectangular room is 6 meters longer than it is wide, and its perimeter is
24 meters. Find the dimension of the room.
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let W be the width of the room, in meters.
Then the length is W + 6 meters.

For the perimeter, we have this equation

(W+6) + W + (W+6) + W = 24,  or

4W + 12 = 24,  or  4W = 24 - 12 = 12.

Then W = 12%2F4 = 3 m

So we found the width W = 3 meters.

Then the length is W+6 = 3+6 = 9 m.

Answer.  The length is 9 m.  The width is 3 m.

For many other similar solved problems see the lessons
    - Solved problems on the perimeter and side lengths of a triangle
    - Solved problems on the perimeter and side lengths of a right-angled triangle
    - Solved problems on the perimeter and the side lengths of a parallelogram
    - Solved problems on the perimeter and side lengths of a rectangle
in this site.

Read these lesson and be trained in solving these problems.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x for length
y for width
p for perimeter, given

x=y%2B6
-
2x%2B2y=p
2%28y%2B6%29%2B2y=p
2y%2B12%2B2y=p
4y%2B12=p
4y=p-12
highlight%28y=%28p-12%29%2F4%29


You do the rest.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +W+ = the width of the room in meters
+W+%2B+6+ = the length of the room in meters
-------------------
The formula for perimeter +P+ is:
+P+=+2W+%2B+2L+
and, for this problem,
+L+=+W+%2B+6+ and
+P+=+24+
+P+=+2W+%2B+2%2A%28+W+%2B+6+%29+
+24+=+2W+%2B+2W+%2B+12+
+4W+=+12+
+W+=+3+
and
+W+%2B+6+=+3+%2B+6+
+W+%2B+6+=+9+
-------------------
the dimensions of the room are 3 x 9
------------
check:
+P+=+2W+%2B+2L+
+P+=+2%2A3+%2B+2%2A9+
+P+=+6+%2B+18+
+P+=+24+
OK