1. Let the two perpendicular forces be: $F_1 = A, \qquad F_2 = \frac{A}{2}$

2. Since they are perpendicular, the magnitude of the resultant is found using Pythagoras theorem: $R = \sqrt{F_1^2 + F_2^2}$

3. Substitute the values: $R = \sqrt{A^2 + \left(\frac{A}{2}\right)^2}$

4. Simplify: $R = \sqrt{A^2 + \frac{A^2}{4}} = \sqrt{\frac{5A^2}{4}}$

5. Therefore, $R = \frac{\sqrt{5}A}{2}$

6. Now check the options:

   • A: $\frac{5A}{2}$ ❌
   • B: $\frac{\sqrt{5}A}{4}$ ❌
   • C: $\frac{\sqrt{5}A}{2}$ ✅
   • D: $\frac{\sqrt{5}A^2}{2}$ ❌ (wrong dimension)

Hence, the correct option is C.