A triangle is dilated using a scale factor of 4. The image is then dilated using a scale factor of 3. What scale factor could you use to dilate the original triangle to get the final image?

1 Answer
Nov 27, 2015

For perimeter, the scale factor would be #a/b# for enlargement, where #a# is the perimeter of the dilated triangle and #b# is the perimeter of the smaller triangle.
For area, the scale factor would be #sqrt(x/y)# for enlargement, where #x# is the area of the dilated triangle and #y# is the area of the smaller triangle.

Explanation:

#rarr#If you are referring to perimeter, the scale factor would be 12.

Example:
Perimeter = #15# #cm#
Dilated by scale factor #4 = 60# #cm#
Dilated by scale factor #3 = 180# #cm#

  • To get from #15# #cm# to #180# #cm#, you would use a scale factor of #180-:15=12#.
  • The scale factor is equal to the change in perimeter between the smaller and dilated triangle.
    For example, #5# #cm##*##12# #cm=180# #cm#

#rarr#If you are referring to area, the scale factor would also be 12.

Example:
Area = #4sqrt(3)# #cm^2#
Dilated by scale factor #4 ~~ 110.85# #cm^2#
Dilated by scale factor #3 ~~ 997.66# #cm^2#

  • To get from #4sqrt(3)# #cm^2# to #997.66# #cm^2#, you would use a scale factor of #sqrt(997.66-:4sqrt(3))~~12#
  • The only difference between the perimeter and area is that the change in area between two similar triangles is not equal to the scale factor.
    For example, #4sqrt(3)# #cm##*##12# #cm!=997.56#
  • To get the scale factor for the area between two triangles, you must square root the change in area between the triangles.