To sketch a square inside a circular region such that the length of the square is of the largest possible value, we note that the four vertices of the square will touch the circumference of the circle and thus the length of the diagonal of the square is equal to the diameter of the circle.
Thus, the length of the diagonal of the square = 7 inches.
Let the length of the sides of the square be s, then using pythagoras theorem
[tex] s^{2} + s^{2} =7^2 \\ 2s^2=49 \\ s^2=24.5 \\ s= \sqrt{24.5} \approx 4.95[/tex]
Therefore, the largest possible length of a side of the square to the nearest tenth of an inch is 4.95 inches.
