Final answer:
The radius of the circle with an inscribed square with a perimeter of 30 inches is 3.75 inches.
Step-by-step explanation:
The student is asking about the radius of a circle that has a square inscribed within it.
We are given the perimeter of the square, which is 30 inches, and we want to find the radius of the circle inscribed in the square.
Since we know that the perimeter of a square is four times the length of one of its sides (4a), we can determine that each side of the square is 7.5 inches (30 inches ÷ 4).
Knowing that the diameter of the circle is equal to the side of the square in an inscribed square situation (a = 2r),
we can conclude that the radius is half of the side length of the square, which is 3.75 inches (7.5 inches ÷ 2).