Triangles △abc and △def are similar. find the lengths of the sides of △def, if ab=2 cm, bc=3 cm, ca=4 cm, de=1.5 cm.

If 1 is divided by the sum of y& 4. the result is equal to 3 divided by 4 .find the value of m?

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

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?