Answer:
True is the most reasonable than False.
Step-by-step explanation:
If we go by "logic", we know that radius and anything that tells you how long, how far, how tall, etc; the value must always be positive.
The area of circle is expressed as:
[tex] \displaystyle \large{A = \pi {r}^{2} }[/tex]
Where r = radius
Since we know that radius cannot be negative going with logic and real basic geometry, the only radius that satisfies A = 9π is r = 3.
[tex] \displaystyle \large{A = \pi {3}^{2} } \\ \displaystyle \large{A = 9\pi }[/tex]
Now if we do not go by logic of real basic geometry, such as length being negative and all.
Since A = 9π, substitute A = 9π in.
[tex] \displaystyle \large{9\pi = \pi {r}^{2} }[/tex]
Divide both sides by π.
[tex] \displaystyle \large{ \frac{9\pi}{\pi} = \frac{\pi {r}^{2} }{\pi} } \\ \displaystyle \large{ 9 = {r}^{2} }[/tex]
Square both sides, adding plus-minus, apply QE.
[tex] \displaystyle \large{ \pm \sqrt{9} = \sqrt{ {r}^{2} } } \\ \displaystyle \large{ \pm 3 = r}[/tex]
So r = ±3 or radius = +3 and -3
So r can be both 3 or -3 if we do not follow logic itself.
However, the answer should be true instead of false as radius being only positive sounds more logical and reasonable rather than radius being negative.
