Why was the princess rescued in the first place?

In the 1977 movie release of Star Wars Episode IV, why was the princess rescued in the first place?

As the required information was with the droid and a lot of time had passed since she was captured, there was a high probablity that she was already dead.

Even if she was to be rescued, why not do both the missions - rescuing the princess and destroying the weapon at the same time?