Suppose a polygon is dilated by a scale factor of k. Write an expression for the ratio of the perimeters. Then, write expression to represent ratio of areas.

Question

 This is a dilation and proportion problem. Please help!!! I really don't get this.

Answer 1

The main thing to remember is that the perimeter scales linearly with the dilation factor and the area scales as the square of the dilation factor.  

 

Imagine a rectangle that is X by Y.  The perimeter P = 2X + 2Y and the area A = XY.  

 

If you scale the rectangle by k then the rectangle will be kX by kY.  

 

The new perimeter will be 2(kX) + 2(kY) = k(2X + 2Y) = kP

The new area will be A = (kX)(kY) = k²XY = k²A.  

 

These scaling rules will work with any polygon but they're easiest to visualize with rectangles.