Answer: The perimeter of rectangle M'N'O'P' =54 cm
Step-by-step explanation:
When we dilated a figure , then the image is the similar figure them the original.
For similar figures,
[tex]\dfrac{\text{Area of original figure}}{\text{Area of image}}=\dfrac{(\text{perimeter of original figure})^2}{(\text{perimeter of image})^2}[/tex]
As per given, Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm².
Area of M'N'O'P' = 126 cm²
then,
[tex]\dfrac{14}{126}=\dfrac{18^2}{(\text{(perimeter of M'N'O'P'})^2}\\\\\Rightarrow\ \text{(perimeter of M'N'O'P'})^2=\dfrac{324}{14}\times126\\\\\Rightarrow\ \text{(perimeter of M'N'O'P'})^2=2916\\\\\Rightarrow\ \text{perimeter of M'N'O'P'}=\sqrt{2916}=54[/tex]
Hence, the perimeter of rectangle M'N'O'P' =54 cm
