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

Answer:

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