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.

A rectangular room is 4 meters longer than it is wide and its perimeter is 24 meters Find the dimension of the roomThe length is meters and the width is meters class=

Respuesta :

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.

[tex]L=4+W[/tex]

The perimeter of a rectangular shape is given by

[tex]P=2(L+W)[/tex]

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

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

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

[tex]\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}[/tex]

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.

[tex]L=45+W[/tex]

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

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

So, the width of the rectangle is 241.25 meters.

[tex]\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}[/tex]

So, the length of the rectangle is 286.25 meters

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