Question

The world's largest swimming pool is the Orthalieb pool in Casablanca, Morocco the length is 30 m longer then 6 times the width. If the perimeter of the pool is 1110 Meters what are the dimensions of the pool?

Answer 1

The length of the rectangular pool is 30m longer than 6 times the width.

Let "x" represent the length of the width, then you can express the dimensions of the pool as follows:

`\begin{gathered} w=x \\ l=6x+30 \end{gathered}`

The perimeter of the pool is 1110m, this perimeter was obtained using the formula:

`P=2w+2l`

Replace the formula with the expressions determined for the width and length:

`1110=2(x)+2(6x+30)`

From this expression, you can determine the value of x:

-First, distribute the multiplications on the right side of the equation:

`\begin{gathered} 1110=2x+2\cdot6x+2\cdot30 \\ 1110=2x+12x+60 \\ 1110=14x+60 \end{gathered}`

-Second, pass 60 to the left side of the equal sign by applying the opposite operation to both sides of it:

`\begin{gathered} 1110-60=14x+60-60 \\ 1050=14x \end{gathered}`

-Third, divide both sides of the equation by 14 to determine the value of x:

`\begin{gathered} (1050)/(14)=(14x)/(14) \\ 75=x \end{gathered}`

The width of the pool is w= 75 meters

Now you can determine the length of the pool:

`\begin{gathered} l=6x+30 \\ l=6\cdot75+30 \\ l=480 \end{gathered}`

The length of the pool is l=480 meters