Question

A circle is inscribed in a square. The area of the circle is 507 square inches. What is the length of each side of the square? Use 3 for pi.

Answer 1

The length of each side of the square is 18 inches.

Step-by-step explanation:

To find the length of each side of the square, we need to find the diameter of the circle. Since the area of the circle is given as 507 square inches, we can use the formula for the area of a circle to find the radius. Area of circle = πr². Substituting the value of the area (507) and assuming π = 3, we get: 507 = 3r². Solving for r, we find that the radius is approximately 9 inches. Since the radius is half the diameter, the diameter of the circle is 2 * 9 = 18 inches. Since the circle is inscribed in a square, the diameter of the circle is equal to the length of each side of the square. Therefore, the length of each side of the square is 18 inches.

Answer 2

26 inches

Step-by-step explanation:

We are given;

• An inscribed circle whose area is 407 square inches
• In this case, we need to know that an inscribed in a square touches the four sides of the triangle.
• Therefore, the diameter of the circle is equivalent to the side of the square.

We are given the area as 507 square inches

But;

Area of the circle = pi × r²

Thus we can get the radius of the circle;

Thus;

507 in² = 3 × r²

r² = (507 ÷ 3)

= 169

r =√169

= 13 inches

But, Diameter = 2 r

Thus; Diameter = 2 × 13

= 26 inches

But, in this case, diameter = side of the square

Therefore, the side of the square is 26 inches