Question

Find the measure of BC.

Answer 1

The two sides stemming from the vertex A, are both equal, each one is 25 units long, since the triangle has twin sides, that means is an "isosceles" triangle.

Now, the twin sides, make twin angles at the base, namely at BC.

and running the angle bisector AD, will not only cut the ∡A in two equal halves, but will also cut the segment BC into two equal halves.  Because the bisector is perpendicular to the base.

all that rant.... simply means that BD = DC or 3x + 4 = 4x - 5.

9 = x.

how long is BC?  well since BC = BD + DC, then  3(9) + 4    +    4(9) - 5.