Final answer:
To find the length of the side of a regular hexagon inscribed in a circle with an area of 49 min², we first find the radius of the circle using the formula A = πr^2. Then, we use the formula s = 2r to find the length of a side of the hexagon.
Step-by-step explanation:
To find the length of the side of a regular hexagon inscribed in a circle, we first need to find the radius of the circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the area of the circle is given as 49 min². So, we can set up the equation 49 = πr^2.
Simplifying the equation, we divide both sides by π: r^2 = 49/π. Taking the square root of both sides gives us r = √(49/π).
Now that we have the radius of the circle, we can find the length of the side of the regular hexagon. In a regular hexagon, all sides are equal in length. The formula to find the length of a side of a regular hexagon inscribed in a circle is s = 2r, where s is the length of a side and r is the radius of the circle. Substituting the value of the radius we found earlier, we get s = 2 * √(49/π).
Simplifying further, we can rationalize the denominator and express the answer in terms of π: s = 2 * √(49π/π) = 2 * √(49π)/√(π) = 2 * 7√π/√π = 14 min.