Question 752580
WHAT YOU NEED TO KNOW:
if the ratio of lengths of sides (or any other measurement) of similar figures on a plane or 3-D solids is {{{k}}},
the ratio of areas of corresponding surfaces is {{{k^2}}}, andthe ratio of corresponding volumes is {{{k^3}}},
and viceversa.
 
In this case the ratio of atras is
{{{area_of_small_triangle/area_of_large_triangle=144/81=12^2/9^2=(12/9)^2)}}}
it must be that
{{{base_of_small_triangle/base_of_large_triangle=k}}} and
{{{k^2=(12/9)^2}}} --> {{{k=12/9}}}
So {{{base_of_small_triangle/base_of_large_triangle=12/9}}}
and since {{{base_of_large_triangle=30}}}
{{{base_of_small_triangle/30=12/9}}} --> {{{base_of_small_triangle=30*12/9}}} --> {{{highlight(base_of_small_triangle=40)}}}