Hey everyone hru and i hope u all are doing good

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=4 and hc=1, find bh.

The following division is being performed using multiplication by the reciprocal find the missing numbers is 5/12 divided by x/3 equals 5/12 times x/10 equals 1/x

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?