Question

question 1 of 15, step 1 of 1 a square is inscribed within a circle with radius r = 30 meters. find the length of one side of the square. express your answer as a simplified radical expression or a decimal rounded to the nearest hundredth. answer

Explanation:

Step1: Recall circle - square relationship

The diameter of the circle is the diagonal of the square. Given $r = 30$ meters, the diameter $d=2r = 60$ meters.

Step2: Use Pythagorean theorem

Let the side - length of the square be $s$. For a square, if the diagonal is $d$, by the Pythagorean theorem $d^{2}=s^{2}+s^{2}=2s^{2}$. Since $d = 60$, we have $60^{2}=2s^{2}$, so $3600 = 2s^{2}$.

Step3: Solve for $s$

First, divide both sides of the equation $3600 = 2s^{2}$ by 2: $s^{2}=\frac{3600}{2}=1800$. Then, take the square - root of both sides: $s=\sqrt{1800}$. Simplify $\sqrt{1800}=\sqrt{900\times2}=30\sqrt{2}\approx30\times1.414 = 42.43$ meters.

Answer:

$30\sqrt{2}\approx42.43$ meters