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%
