$\begin{array}{l}\text{Here, we can write it as}\\ \\ {\text{= ?}}^{\text{2}}{\text{+ 420 = (199)}}^{\text{2}}-\text{{ (72 )2 + (61)2}}\\ \\ {\text{= ?}}^{\text{2}}\text{+ 420\hspace{0.17em}= 39601}-\text{{5184 + 3721}}\\ \\ {\text{= ?}}^{\text{2}}\text{+ 420 = 39601}-\text{{8905}}\\ \\ {\text{= ?}}^{\text{2}}\text{+ 420 = 30696}\\ \\ \text{= ? 2 = 30696}-\text{420}\\ \\ \text{= ? 2 = 30276}\\ \\ \text{? = }\sqrt{\text{30246}}\text{ = 174}\end{array}$

Hence, Option E is correct.