Area of triangle $$A B C=15 \sqrt{2}$$

$$\begin{aligned} & \Rightarrow \frac{1}{2}|\overline{A B} \times \overline{A C}|=15 \sqrt{2} \quad \text{.... (i)}\\ & \quad \overline{A B} \times \overline{A C}\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & -7 \\ 6 & d & -2 \end{array}\right| \\ & =(7 d-4) \hat{i}-40 \hat{j}+(d-12) \hat{k} \quad \text{... (ii)} \end{aligned}$$

From (i) and (ii) $$5 d^2-8 d-4=0$$

$$\Rightarrow d=\frac{-}{5}$$ (Rejected) or $$d=2$$

Also, $$\overline{A B}+\overline{B C}=\overline{A C}$$

$$\begin{aligned} & \Rightarrow a+1=6 \Rightarrow a=5 \\ & b+2=d \Rightarrow b=0 \end{aligned}$$

and $$c-7=-2 \Rightarrow c=5$$

$$|\overline{A B}|=\sqrt{54},|\overline{A C}|=\sqrt{44},|\overline{B C}|=\sqrt{50}$$

Largest side has length of $$\sqrt{54}$$ units