Respuesta :
The tile should Orchid choose, to minimize costs, is rectangular tiles. The total cost will be $8 less.
What is the area of square and rectangle?
Area of square is the square of its sides length. Area of rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length rectangle and (b) is the width of the rectangle.
Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles.
The square tile is One-half foot by One-half foot. Thus, the area of square tile is,
[tex]A=\left(\dfrac{1}{2}\right)^2\\A=\dfrac{1}{4}\rm ft^2[/tex]
Total square tiles required for 40 square feet area,
[tex]n=\dfrac{40}{\dfrac{1}{4}}\times\\n=160[/tex]
Square tile costs $0.45 per tile. Thus, the cost of 160 square tile is,
[tex]C_s=0.45\times160\\C_s=72[/tex]
The rectangular tile is 2 feet by One-fourth foot. Thus the area of thios tile is,
[tex]A_r=2\times\dfrac{1}{4}\\A_r=\dfrac{1}{2}\rm\;ft^2[/tex]
Number of rectangular tiles required for 40 square feet area,
[tex]n=\dfrac{40}{\dfrac{1}{2}}\\n=80[/tex]
The cost of this tile is $0.80 per tile. Thus, the cost of 80 rectangle tiles is,
[tex]C_s=0.8\times80\\C_s=64[/tex]
Hence, the cost of rectangular tile is $8 less than the square tile.
Thus, the tile should Orchid choose to minimize costs, is rectangular tiles. The total cost will be $8 less.
Learn more about the area of square here;
https://brainly.com/question/1658516
