Question

A rectangular bathroom floor is covered with square tiles that are 1 LaTeX: \frac{1}{2}1 2 feet by 1 LaTeX: \frac{1}{2}1 2 feet. The length of the bathroom floor is 10 LaTeX: \frac{1}{2}1 2 feet and the width is 6 LaTeX: \frac{1}{2}1 2 feet. a) How many tiles does it take to cover the length of the floor?

Answer 1

273 tiles

Explanation:

Given

Square tile

`Side=(1)/(2) ft`

Bathroom floor

`Length = 10(1)/(2)ft`

`Width = 6(1)/(2)ft`

Required

Determine the number of tiles to cover the floor

First, we calculate the area of the floor:

`A_(floor) = Length * Width`

`A_(floor) = 10(1)/(2) * 6(1)/(2)`

Convert to decimals

`A_(floor) = 10.5 * 6.5`

`A_(floor) = 68.25ft^2`

Next, we calculate the area of the square tile:

`A_(tile) = Side * Side`

`A_(tile) = (1)/(2) * (1)/(2)`

Convert to decimal

`A_(tile) = 0.5 * 0.5`

`A_(tile) = 0.25ft^2`

The number of tiles is then calculated as:

`Tiles = (A_(floor))/(A_(tile))`

`Tiles = (68.25ft^2)/(0.25ft^2)`

`Tiles = (68.25)/(0.25)`

`Tiles = 273`