Let ABC be a triangle of area $15 \sqrt{2}$ and the vectors $\overrightarrow{\mathrm{AB}}=\hat{\imath}+2 \hat{\jmath}-7 \hat{k}, \overrightarrow{\mathrm{BC}}=a \hat{\imath}+b \hat{\jmath}+c \hat{k}$ and $\overrightarrow{\mathrm{AC}}=6 \hat{\imath}+ d \hat{\jmath}-2 \hat{k}, d>0$. Then the square of the length of the largest side of the triangle $A B C$ is