Find the perimeter of the rectangle after dilation.

Question

A rectangle with a perimeter of 147 units is dilated by a scale factor of 3/4. Find the perimeter of the rectangle after dilation. Round your answer to the nearest tenth, if necessary.

Answer 1

Hi Roman -

When we dilate a shape by a particular scale factor, it means that all of the sides of the shape will have their lengths multiplied by that number. For example, if we had a square with sides of length 40, a 3/4 dilation would mean that all side lengths get multiplied by 3/4, leaving us with a square with sides of length 30 after the dilation. The convenient thing that this means is that the perimeter of a shape will also change by the scale factor of the dilation as well since all the sides are changing by that same scale factor - in the example above, the orignal perimeter of the square was 4*40 = 160, and after the dilation it would be 4*30 = 120. Notice how we could just multiply the original perimeter, 160, by the scale factor, 3/4, to get 120, without worrying about scaling the sides individually.

Therefore, all we need to do for this problem is multiply the perimeter 147 by the scale factor 3/4, and we're there, even though we don't know anything about the lengths of the sides of this rectangle:

147 * (3/4) = 110.25, which you can round up to the nearest tenth and get 110.3.

Hope this helps! Let me know if you have any other questions and I can explain more.