Question

A rectangular room is 4 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

We are given the following information

Perimeter of the rectangular room = 24 meters

The rectangular room is 4 meters longer than it is wide.

Let L be the length and W be the width of the rectangular room.

`L=4+W`

The perimeter of a rectangular shape is given by

`P=2(L+W)`

Substitute P = 24 and L = 4 + W into the above equation

`\begin{gathered} P=2(L+W) \\ 24=2(4+W+W) \\ 24=2(4+2W) \\ 24=8+4W \\ 24-8=4W \\ 16=4W \\ (16)/(4)=W \\ W=4\;m \end{gathered}`

So, the width of the rectangular room is 4 meters.

`\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}`

So, the length of the rectangular room is 8 meters.

Length = 8 meters

Width = 4 meters

Example Problem:

Suppose that perimeter is 1055 meters.

The length is 45 meters longer than the width of the rectangle.

`L=45+W`

Now, substitute P = 1055 and L = 45 + W into the equation for the perimeter of the rectangle.

`\begin{gathered} P=2(L+W) \\ 1055=2(45+W+W) \\ 1055=2(45+2W) \\ 1055=90+4W \\ 1055-90=4W \\ 965=4W \\ W=(965)/(4) \\ W=241.25\;m \end{gathered}`

So, the width of the rectangle is 241.25 meters.

`\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}`

So, the length of the rectangle is 286.25 meters