The length of side x in the smaller rectangle, given that the two rectangles are similar, is found to be 6 inches using the proportion of corresponding sides.
To find the length of side x, we can set up a proportion since the two rectangles are similar. The ratio of corresponding sides in similar figures is equal. In this case, we can set up the following proportion:
(length of the larger rectangle) / (breadth of the larger rectangle) = (length of the smaller rectangle) / (breadth of the smaller rectangle)
Substitute the given values:
7.5 / 4 = x / 3.2
Now, solve for x:
x = (7.5 × 3.2) / 4 = 6
Therefore, the length of side x is 6 inches.