Question

Thomas used 25 square tiles to cover a patio with an area of 75 square feet. Paul used 20 square tiles to cover a patio with an area of 100 square feet. Sarah used 30 square tiles to cover a patio with an area of 120 square feet. Who used the square tile with the greatest side length, and what was its side length to the nearest hundredth ?

Answer 1

Answer: Paul used the square tile with the greatest side length. Its side length (to the nearest hundredth) was
`2.24\ ft`

Explanation:

The side lenght "s" of a square can be calculated with this formula:

`s=√(A)`

Where "A" is the area.

We know that Thomas used 25 square tiles to cover a patio with an area of 75 square feet, then, the area of each 1 tile was:

`A_(tile)=(75)/(25)=3\ ft^2`

Its side lenght, rounded to the nearest hundreth,was:

`s=√(3\ ft^2)=1.73\ ft`

Paul used 20 square tiles to cover a patio with an area of 100 square feet, then, the area of each 1 tile was:

`A_(tile)=(100)/(20)=5\ ft^2`

Its side lenght, rounded to the nearest hundreth,was:

`s=√(5\ ft^2)=2.24\ ft`

Sarah used 30 square tiles to cover a patio with an area of 120 square feet, then, the area of each 1 tile was:

`A_(tile)=(120)/(30)=4\ ft^2`

Its side lenght, rounded to the nearest hundreth,was:

`s=√(4\ ft^2)=2\ ft`

Therefore, Paul used the square tile with the greatest side length. Its side length (to the nearest hundredth) was
`2.24\ ft`