$\begin{equation} \left.\begin{aligned}        {F_{net}} = ma = m \times \frac{{25}}{2}\\        F_{net}^2 = F_1^2 + F_2^2       \end{aligned} \right\} \end{equation}   \Rightarrow {(m \times \frac{{25}}{2})^2} = {(\frac{3}{4})^2} + {(10m)^2}$ $ \Rightarrow {m^2} \times \frac{{625}}{4} - 100{m^2} = \frac{9}{{16}} \Rightarrow \frac{{225}}{4}{m^2} = \frac{9}{{16}} \Rightarrow \frac{{15}}{2}m = \frac{3}{4} \Rightarrow m = 0/1kg = 100g$