Question

Stagg high school has a rectangular swimming pool. The area of the water in the pool is 1250 meters squared. The Length is twice the width. If the length is 2x and the width is x, please following:

Answer 1

Stagg high school has a rectangular shape pool. We will go ahead and declare variables for the dimensions of the rectangular pool as follows:

`\begin{gathered} \text{Length = L} \\ side\text{ = w} \end{gathered}`

The following data is given to us about the pool:

" The area of the water in the pool is 1250 meters squared. "

We will go ahead and decrypt the above statement into a mathematical form. We will use the formula for expressing the area ( A ) of a rectangle that will model the pool at Stagg high school as follows:

`\begin{gathered} A\text{ = L}\cdot w,Given\colon A=1250m^2 \\ \textcolor{#FF7968}{L\cdot w}\text{\textcolor{#FF7968}{ = 1250 }}\textcolor{#FF7968}{\ldots Eq1} \end{gathered}`

We have expressed the area given for the rectangular pool ( A ) in terms of its dimensions ( Length - L and width - w ) as given in Eq1.

The next statement relates the dimensions of the rectangular pool given as:

" The Length is twice the width. If the length is 2x and the width is x "

The above statement tells us how big or how long the length of the pool ( L ) is with respect to the width ( w ) of the pool. We will go ahead and decrypt the above statement into a mathematical form as follows:

`\textcolor{#FF7968}{L}\text{\textcolor{#FF7968}{ = 2w }}\textcolor{#FF7968}{\ldots Eq2}`

We were given two pieces of information regarding the pool at Stagg high-school. We have decryted each statement into a mathematical form using the standard defined dimensions of shape ( rectangle ) of the pool.

The two equations are as such:

`\begin{gathered} L\cdot w\text{ = 1250 }\ldots\textcolor{#FF7968}{Eq1} \\ L\text{ = 2w }\ldots\text{ }\text{\textcolor{#FF7968}{Eq2}} \end{gathered}`

We have two equations ( Eq1 and Eq2 ) and two dimensional variables ( L and w ). We can solve these two equations simultaneously using the susbtitution method as follows:

- Substitute Eq2 into Eq1 and solve for w:

`\begin{gathered} (2w\text{ ) }\cdot\text{ w = 1250} \\ w^2\text{ = 625} \\ w\text{ = }√(625) \\ \textcolor{#FF7968}{w=}\text{\textcolor{#FF7968}{ 25 meters}} \end{gathered}`

- Back substitute the value of w into Eq 2:

`\begin{gathered} L\text{ = 2}\cdot w \\ L\text{ = 2}\cdot25 \\ \textcolor{#FF7968}{L}\text{\textcolor{#FF7968}{ = 50 meters}} \end{gathered}`

The dimensions of the rectangular pool at Stagg high-school are as follows:

Length ( L ) = 50 meters

Width ( w ) = 25 meters