A square is inscribed In a circle with radius 6 inches. what is the perimeter of the square in inches? help pls

The perimeter of the square in inches is 48 square inches

The diameter of the circle is twice the given radius

Given the following:

radius = 6√2

diameter = 2(6√2)

diameter = 12√2

The diagonal of the cube inscribed will be equal to the diameter of the circle.

Next is to get the side length "l" of the square using the Pythagoras theorem. According to the theorem:

l²+l² = (12√2)²

2l² = 144(2)

l² = 288/2

Take the square root of both sides

l² = 144

l = √144

l = 12inches

Next is to get the perimeter of the square

Perimeter of the square = 4L

Perimeter of the square = 4(12)

Hence the perimeter of the square is 48 square inches

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48 in

Step-by-step explanation:

The diagonal of the inscribed square equals the diameter of the circle.

1. Calculate the diagonal of the square

d = 2r = 2 × 6√2 in =12√2 in

2. Calculate the side of the square

∆ACB is an isosceles right triangle.

We can use Pythagoras' Theorem to calculate the length of a side s.

3. Calculate the perimeter of the square

P = 4s = 4 × 12 in = 48 in

The perimeter of the square is 48 in.

step-by-step explanation: