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: Paul used the square tile with the greatest side length. Its side length (to the nearest hundredth) was [tex]2.24\ ft[/tex]Step-by-step explanation: The side lenght "s" of a square can be calculated with this formula: [tex]s=\sqrt{A}[/tex] 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: [tex]A_{tile}=\frac{75}{25}=3\ ft^2[/tex] Its side lenght, rounded to the nearest hundreth,was: [tex]s=\sqrt{3\ ft^2}=1.73\ ft[/tex] Paul used 20 square tiles to cover a patio with an area of 100 square feet, then, the area of each 1 tile was: [tex]A_{tile}=\frac{100}{20}=5\ ft^2[/tex] Its side lenght, rounded to the nearest hundreth,was: [tex]s=\sqrt{5\ ft^2}=2.24\ ft[/tex] Sarah used 30 square tiles to cover a patio with an area of 120 square feet, then, the area of each 1 tile was: [tex]A_{tile}=\frac{120}{30}=4\ ft^2[/tex] Its side lenght, rounded to the nearest hundreth,was: [tex]s=\sqrt{4\ ft^2}=2\ ft[/tex] Therefore, Paul used the square tile with the greatest side length. Its side length (to the nearest hundredth) was [tex]2.24\ ft[/tex]