A square fits exactly inside a circle with each of its vertices being on the circumference of the circle.
The square has sides of length x cm.
The area of the circle is 56cm squared.
Work out value of x.
Give answer correct to 3 significant figures.

Respuesta :

Answer:

The side of the square is 5.971 cm

Step-by-step explanation:

If the square fits the circle exactly, then its diagonal is equal to the diameter of the circle. Since the side of the square has a length of [tex]x[/tex] cm, then it's diagonal have the length of [tex]x\sqrt2[/tex] cm. Using the circle's area we can find the diagonal of the square, as shown below:

[tex]area = \pi*r^2\\56 = pi*r^2\\r^2 = \frac{56}{\pi}\\r = \sqrt{\frac{56}{\pi}}\\r = 4.222[/tex]

Since the diameter of the circle is the same as the diagonal of the square, then:

[tex]x\sqrt{2} = 2*r \\x = \frac{2*r}{\sqrt{2}}\\x = \frac{2*4.222}{\sqrt{2}}\\x = 5.971[/tex]

The side of the square is 5.971 cm

Answer:

5.97

Step-by-step explanation: