Dilations and Measurement

Tom's vegetable garden currently measures 10 ft by 10 ft. Tom w ants to change the size of his garden and will either use a scale factor of 2 or 1/2. Complete the following questions to observe how each scale factor would change the perimeter and the area of his garden.

What do you notice?

What happened to the perimeter when Tom used a scale factor of 2?

What happened to the area?

What do you notice?

What happened to the perimeter when Tom used a scale factor of 1/2?

What happened to the area?

The need to know

When a figure is dilated by a scale factor of "x", its area changes by a factor of x^2.

Its perimeter changes by a factor of x.

Example

If a figure is dilated by a scale factor of 10, its area will change by a factor of 10² (100) and its perimeter will change by a factor of 10.

Original area: 49 ft² Original perimeter: 28 ft
New area:_____ ft² New perimeter:______ ft