many geometric problems require a bit of algebra. for example, if you want to find the missing side of a right triangle where the hypotenuse is 160 and the other leg is 77, that requires knowledge of both geometry and algebra.

I wonder maybe could it have been possible that although algebra wasn't invented that without realizing it the same kind of methods of problem solving were used? And could it have been that algebra was established because of it's use in solving geometric problems?