Given the right triangles $ABC$ and $ABD$, what is the length of segment $BC$, in units?

Answer 1

Since $\overline{BC}$ and $\overline{BD}$ are corresponding medians in right triangles $ABC$ and $ABD$, we have $BC = 2BD$. Because $\overline{AB}$ and $\overline{AD}$ are congruent in isosceles triangles $ABC$ and $ABD$, we have $BD = AB = 14$ units so $BC = 2BD = \boxed{28}$ units. [asy]
pair A,B,C,D;
A = (0, 14);
B = (-21,0);
C = (0, 0);
D = (14,0);
draw(A--B--C--cycle);
draw(A--D--B);
label("$A$",A,N);
label("$B$",B,SW);
label("$C$",C,S);
label("$D$",D,S);[/asy]