The area of a circle is:
A = pi * (d / 2) ^ 2
A = (1/4) * pi * (d) ^ 2
Where,
d: diameter of the circle.
By clearing the diameter we have:
D = sqrt (4A / pi) if the area increases 50% we have:
D '= sqrt (4 * (1.5 * A) / pi)
Rewriting:
D '= sqrt (1.5) * sqrt (4 * A / pi) = sqrt (1.5) * D
The new diameter is:
D '= sqrt (1.5) * D
The percentage increase is:
[sqrt (1.5) -1] * 100% = 22.47%
Answer:
The diameter of a circle must be increased 22.47% to increase its area by 50%