Find the ratio between the fourth proportional of 42, 56, 63 and the fourth proportional of 189, 273, and 153.

Let x be the fourth proportional of 42, 56, and 63:
56
42
​
=
x
63
​
⟹
4
3
​
=
x
63
​
⟹x=
3
63×4
​
=21×4=84
Let y be the fourth proportional of 189, 273, and 153:

273
189
​
=
y
153
​

Simplifying
273
189
​
by dividing by 21:

13
9
​
=
y
153
​
⟹y=
9
153×13
​
=17×13=221
Now, finding the ratio between x and y:

Ratio=x:y=84:221