Question

A square is inscribed In a circle with radius 6\sqrt{2} " alt=" \sqrt{2} " align="absmiddle" class="latex-formula">
inches. what is the perimeter of the square in inches? help pls​

Answer 1

Answer:

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.

$\begin{array}{rcl}s^{2} + s^{2} & = & (12\sqrt{2})^{2}\\2s^{2} & = & 144 \times 2\\s^{2} & = & 144\\s & = & \text{12 in}\\\end{array}$

3. Calculate the perimeter of the square

P = 4s = 4 × 12 in = 48 in

The perimeter of the square is 48 in.