Questions: The perimeter of the dilated rectangle will be times the perimeter of the original rectangle. The area of the dilated rectangle will be times the area of the original rectangle. A pentagon is dilated by a scale factor of 0.5. The perimeter of the dilated pentagon will be times the perimeter of the original pentagon. The area of the dilated pentagon will be times the area of the original pentagon. A hexagon is dilated by a scale factor of 2/7 The perimeter of the dilated hexagon will be times the perimeter of the original hexagon.

Solution Steps

To solve these problems, we need to understand the effect of dilation on the perimeter and area of geometric shapes. When a shape is dilated by a scale factor \( k \):

1. The perimeter of the dilated shape will be \( k \) times the perimeter of the original shape.
2. The area of the dilated shape will be \( k^2 \) times the area of the original shape.

Let's apply this to the given shapes and scale factors.

1. For the pentagon dilated by a scale factor of 0.5:

   • The perimeter of the dilated pentagon will be \( 0.5 \) times the perimeter of the original pentagon.
   • The area of the dilated pentagon will be \( (0.5)^2 = 0.25 \) times the area of the original pentagon.

2. For the hexagon dilated by a scale factor of \( \frac{2}{7} \):

   • The perimeter of the dilated hexagon will be \( \frac{2}{7} \) times the perimeter of the original hexagon.

For the pentagon dilated by a scale factor of \( k = 0.5 \):

• The perimeter of the dilated pentagon will be \( 0.5 \) times the perimeter of the original pentagon.
• The area of the dilated pentagon will be \( (0.5)^2 = 0.25 \) times the area of the original pentagon.

For the hexagon dilated by a scale factor of \( k = \frac{2}{7} \):

• The perimeter of the dilated hexagon will be \( \frac{2}{7} \) times the perimeter of the original hexagon.

Final Answer