Question

Maria's family has an underground pool with tile around the edge. Using the information on the diagram, find the following:

Answer 1

0. 6x+20

,

1. 15x+25 square feet

,

2. 200 square feet

,

3. 175 square feet

,

4. $218.75

Step-by-step explanation:

Part 1

The length of the pool with the tile = 2x+5 ft

The width of the pool with the tile = x+5 ft

`\begin{gathered} \text{Perimeter}=2(l+w) \\ =2(2x+5+x+5) \\ =2(3x+10) \\ =6x+20\text{ ft} \end{gathered}`

Part 2 (The area of just the tile)

`\begin{gathered} \text{Area of just the tile = Area of the outer rectangle - Area of the pool} \\ =(2x+5)(x+5)-(2x)(x) \\ \text{Expand} \\ =2x^2+10x+5x+25-2x^2 \\ =15x+25\text{ square feet} \end{gathered}`

Part 3

If x=10

`\text{Area of the pool}=(2x)(x)=(2*10)(10)=200ft^2`

Part 4

From part 2, the area of the tiles = 15x+25

If x=10

`\text{Area of the tile}=15(10)+25=150+25=175ft^2`

Part 5

The area of the tile = 175 square foot

If the tile costs $1.25 per square foot

The amount needed to replace the tiles will be:

`175ft^2*(\$1.25)/(ft^2)=\$218.75`