Answer:
6.4 inches
Explanation:
The diagonal of a square is equal to the diameter of the circle that can be inscribed in the square. So, if we can find the diameter of the circle, we can then find the length of the square's diagonal, which is also the largest possible length of a side of the square.
The diameter of the circle is 9 inches, so the radius is 4.5 inches. The diagonal of the square is the diameter of the circle, which is 9 inches.
Let's use the Pythagorean theorem to find the length of a side of the square:
a^2 + b^2 = c^2
where a and b are the sides of the square and c is the diagonal.
We know c = 9, so:
a^2 + b^2 = 9^2 = 81
Since we want the largest possible length of a side of the square, we want to maximize the value of a. In a square, a and b are equal, so we can simplify the equation to:
2a^2 = 81
a^2 = 40.5
a ≈ 6.4 (rounded to the nearest tenth of an inch)
Therefore, the largest possible length of a side of the square is approximately 6.4 inches.