Triangle rst was dilated by a scale factor of . the image, triangle r's't', is an isosceles triangle, with each leg measuring 8 units.

what is the length of a leg of the pre-image, triangle rst?

Triangle RST was dilated by a scale factor of 1/2

Given: triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. 

Pre-image: 
measure of pre-image * scale factor = measure of resulting image

measure of pre-image = measure of resulting image / scale factor

measure of pre-image = 8 / 1/2
measure of pre-image = 8 * 2/1 

measure of pre-image = 16 units.