Respuesta :
Stagg high school has a rectangular shape pool. We will go ahead and declare variables for the dimensions of the rectangular pool as follows:
[tex]\begin{gathered} \text{Length = L} \\ side\text{ = w} \end{gathered}[/tex]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:
[tex]\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}[/tex]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:
[tex]\textcolor{#FF7968}{L}\text{\textcolor{#FF7968}{ = 2w }}\textcolor{#FF7968}{\ldots Eq2}[/tex]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:
[tex]\begin{gathered} L\cdot w\text{ = 1250 }\ldots\textcolor{#FF7968}{Eq1} \\ L\text{ = 2w }\ldots\text{ }\text{\textcolor{#FF7968}{Eq2}} \end{gathered}[/tex]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:
[tex]\begin{gathered} (2w\text{ ) }\cdot\text{ w = 1250} \\ w^2\text{ = 625} \\ w\text{ = }\sqrt{625} \\ \textcolor{#FF7968}{w=}\text{\textcolor{#FF7968}{ 25 meters}} \end{gathered}[/tex]- Back substitute the value of w into Eq 2:
[tex]\begin{gathered} L\text{ = 2}\cdot w \\ L\text{ = 2}\cdot25 \\ \textcolor{#FF7968}{L}\text{\textcolor{#FF7968}{ = 50 meters}} \end{gathered}[/tex]The dimensions of the rectangular pool at Stagg high-school are as follows:
Length ( L ) = 50 meters
Width ( w ) = 25 meters
