Scale Factor and Area Comparisons- Inv 3

Reviewing some notes....

Consider a rectangle 5cm by 2cm.

The area of the rectangle is 5cm × 2cm = 10cm², but what happens if the rectangle is enlarged?
We will start by multiplying the lengths by scale factor 2.
The rectangle is now 10cm by 4cm and the area is 40 cm².
The lengths were multiplied by 2, but the area has been multiplied by a scale factor of 4.

Now we will multiply the lengths in the original rectangle by scale factor 3.
The rectangle is now 15cm by 6cm and the area is 90 cm².
The lengths were multiplied by 3, but the area has been multiplied by a scale factor of 9.

Finally, we will try multiplying the lengths by scale factor 5.
The rectangle is now 25cm by 10cm and the area is 250 cm².
The lengths were multiplied by 5, but the area has been multiplied by a scale factor of 25.

See a pattern!?
When all the lengths are multiplied by x (the scale factor) , the areas are multiplied by x² (the scale factor squared).