Respuesta :
Answer:
C. [tex]\sqrt{\pi}[/tex]
Step-by-step explanation:
We have been given that a square region with side x and a circular region with radius r have the same area. We are asked to find that x must be how many times as great as r.
We know that area of a square is square of its each side length, so area of square region with side x would be [tex]x^2[/tex].
We also know that area of circle is [tex]\pi r^2[/tex].
Since we have been given that both areas are same, so we will equate both areas as:
[tex]x^2=\pi r^2[/tex]
Let us take positive square root of both sides as:
[tex]\sqrt{x^2}=\sqrt{\pi r^2}[/tex]
[tex]x=\sqrt{\pi}\cdot \sqrt{r^2}[/tex]
[tex]x=\sqrt{\pi}\cdot r[/tex]
Let us divide both sides by r:
[tex]\frac{x}{r}=\frac{\sqrt{\pi}\cdot r}{r}[/tex]
[tex]\frac{x}{r}=\sqrt{\pi}[/tex]
Therefore, x must be [tex]\sqrt{\pi}[/tex] times greater than r and option C is the correct choice.
