Final answer:
To find the number of grey tiles needed for the second border, we calculate the perimeter of the outer boundary formed by the grey tiles, 4 times 'ft + 2', and then subtract the overcounted corners, resulting in 4ft + 4.
Step-by-step explanation:
In order to determine the total number of grey tiles needed for the second border of tiles around the square fountain area, we need to understand the perimeter concept. Given that the students have been working with squares where the perimeter is 4 times the side length, and the area is the side length squared, we can use these principles to solve the problem.
The side length of the internal square is 'ft' feet. The tiles are laid in two consecutive squares around the fountain. The first square of tiles adds 1 foot to each side, resulting in a side length of 'ft + 1' for the outer boundary of the first row of tiles. The second row of tiles further adds 1 foot to each side of this new square, creating a side length of 'ft + 2' for the outer boundary of the grey tiles.
Therefore, the perimeter of the square formed by the outer boundary of the grey tiles is 4 times 'ft + 2'. This calculation yields: 4(ft + 2) = 4ft + 8. However, since we are only adding 1 tile per side for the corners, we subtract 4 from this total because the corners are counted twice when calculating the perimeter with 1 tile width. Hence, the correct expression for the number of grey tiles needed is: 4ft + 8 - 4 = 4ft + 4.