If the two sides of a rectangle are 12 inches and the other sides 9 inches and a smaller rectangle has larger sides of 4 inches how long are the smaller sides?

We have similar rectangles, here  and the ratio of the sides are the same...so......

Long side of the larger rectangle / short side of the larger rectangle =

Long side of the smaller rectangle / short side of the smaller rectangle

Mathematically, we have......

12/9 = 4/x      cross-multiply

12x = 36    divide both sides by 12

x= 3 inches