Final answer:
The perimeter of the smaller parallelogram is 42.2 cm.
Step-by-step explanation:
The ratio of the sides of two similar parallelograms is 4:9, and the perimeter of the larger parallelogram is 42.3 cm. To find the perimeter of the smaller parallelogram, we can use the property that the ratios of corresponding sides of similar figures are equal. Let's assume the sides of the smaller parallelogram are 4x and 9x, where x is a constant. The perimeter of the smaller parallelogram is 2(4x + 9x), which simplifies to 26x.
To find the value of x, we can set up the equation 26x = 42.3 and solve for x. Dividing both sides by 26, we get x = 1.626. Finally, we can substitute x back into the expression for the perimeter of the smaller parallelogram, giving us a value of 26(1.626) = 42.2 cm.