Answer
The correct answer is (d) $1/\sqrt{2}$
Work Step by Step
The area of the original circle is $A = \pi r^2$
We multiply the radius $r$ by some factor $k$;
The new radius is $kr$.
The area of the new circle is $A_2 = \pi (kr)^2$
We know that $A_2 = \frac{A}{2}$
$\pi (kr)^2 = \frac{\pi r^2}{2}$
$k^2 \pi r^2 = \frac{\pi r^2}{2}$
$k^2 = \frac{1}{2}$
$k = \sqrt{\frac{1}{2}} = 1 / \sqrt{2}$
The correct answer is (d) $1/\sqrt{2}$
