Question

Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm2. After rectangle MNOP is dilated, rectangle M'N'O'P' has an area of 126 cm2. What is the perimeter of rectangle M'N'O'P'?

Answer 1

Answer: The perimeter of rectangle M'N'O'P' =54 cm

Explanation:

When we dilated a figure , then the image is the similar figure them the original.

For similar figures,

`\frac{\text{Area of original figure}}{\text{Area of image}}=\frac{(\text{perimeter of original figure})^2}{(\text{perimeter of image})^2}`

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,

`(14)/(126)=\frac{18^2}{(\text{(perimeter of M'N'O'P'})^2}\\\\\Rightarrow\ \text{(perimeter of M'N'O'P'})^2=(324)/(14)*126\\\\\Rightarrow\ \text{(perimeter of M'N'O'P'})^2=2916\\\\\Rightarrow\ \text{perimeter of M'N'O'P'}=√(2916)=54`

Hence, the perimeter of rectangle M'N'O'P' =54 cm