To complete the table of equivalent ratios of lengths to widths, we need to find the missing values that make the ratios in each row equal to each other. One way to do this is to use cross-multiplication.
First, we can compare the first and second rows to find the value that makes them equivalent:
x/18 = 8/y
Multiplying both sides by 18y, we get:
xy = 144
So the missing value in the first row is 144/18 = 8, and the missing value in the second row is 144/8 = 18.
Next, we can compare the third and fourth rows:
10/30 = 12/z
Multiplying both sides by 30z, we get:
10z = 360
Dividing both sides by 10, we get:
z = 36
So the missing value in the third row is 36, and the missing value in the fourth row is 12/10 * 36 = 43.2.
Therefore, the completed table is:
8 18
8 144/10 = 14.4
10 30
12 36