Problem No$.3$: Failure due to Welds

$(40$ Points$)$ Design the fillet welds on two sides of the angle connected to a gusset plate as shown. The full tensile strength of the angle is to be developed using E$70$ electrodes. Use ASD, A$50$ steel and one weld size only. The lengths of the welds, $L_1$ and $L_2,$ are to be proportioned such that the weld centroid coincides with the centroid of the angle. This way, eccentricities in the weld group can be eliminated, if not minimized. Also, the length $L_1$ must be minimized in order that the size of the gusset plate can likewise be minimized.

Note: Express your answer up to $3$ decimal places.