Answer:
The area of the interior tiles must be 7 inches ² with dimensions 1.871" x 3.742".
Explanation:
Since the interior tiles must be 3.5 larger then the border tiles to calculate the dimensions of the interior tiles we first need to find the area of the border tiles. This is shown bellow:
area border = 1*2 = 2 inches²
The area of the interior tiles is 3.5 larger than that, so we have:
area interior = 2*(area border) = 2*3.5 = 7 inches²
In order to maintain the same proportions as the border tiles we must find a width that is two times the height, so we have:
area interior = width*height = 2*height*height = 2*height²
7 = 2*height²
height² = 3.5
height = sqrt(3.5) = 1.871
width = 2*height = 2*1.871 = 3.74166
The area of the interior tiles must be 7 inches ² with dimensions 1.871" x 3.742".