Question

The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find anexpression for the area of the tiled floor.0 4w2 + 200wO 6w? + 130w + 8000 2W2 + 100WO 4w2 + 200w + 2100

Answer 1

- To understand the question, we simply need to sketch the diagram of the pool and the extra w meters of tiles.

- The formula for the area of a rectangle is given by:

`\begin{gathered} A=l* b \\ l=\text{length} \\ b=\text{breadth} \end{gathered}`

- We can apply this formula to get the area of the pool and the area of the pool plus tiles. These areas, when subtracted, would give us the area of the tiled floor only.

- We can thus solve the question as follows:

1. Area of pool:

`\begin{gathered} A_1=l* b \\ l=70,b=30 \\ A_1=70*30=2100 \end{gathered}`

2. Area of pool plus tiles:

`\begin{gathered} A=l* b \\ l=70+w+w=70+2w \\ b=30+w+w=30+2w \\ \\ \therefore A_2=(70+2w)(30+2w) \\ \text{Expand the bracket} \\ A_2=2100+140w+60w+4w^2 \\ \\ \therefore A_2=4w^2+200w+2100 \end{gathered}`

3. Area of tiles:

`\begin{gathered} \text{Area of tiles}=Area\text{ of pool plus tiles }-\text{ Area of pool} \\ \text{Area of tiles}=A_2-A_1 \\ \text{Area of tiles}=(4w^2+200w+2100)-2100 \\ \text{Area of tiles}=4w^2+200w+2100-2100 \\ \\ \therefore\text{Area of tiles}=4w^2+200w \end{gathered}`

Final Answer

`\text{Area of tiles}=4w^2+200w\text{ (OPTION 1)}`