Question 395122
By connecting the midpoints of AB and AC, you have forme two similar triangles, ABC and AED. Using the fact that in similar triangles, corresponding sides are proportional, we can write:
{{{ED/BC = AD/AC}}}
Substituting: {{{ED = 2x+3}}} and {{{BC = 7x-3}}} we get:
{{{(2x+3)/(7x-3) = AD/AC}}} But, because D is the midpoint of AC, {{{AD = (1/2)AC}}}, so...
{{{(2x+3)/(7x-3) = 1/2}}} Cross-multiplying, we get...
{{{4x+6 = 7x-3}}} Solve for x:
{{{6 = 3x-3}}} 
{{{3x = 9}}}
{{{x = 3}}} so...
{{{ED = 2x+3}}} Substitute x=3.
{{{ED = 9}}} and...
{{{BC = 7x-3}}}
{{{BC = 18}}}