In the diagram below, the area of $\triangle BCD$ is 60. What is the length of side $\overline{BC}$? [asy] size(5cm); pair a=(9,8); pair b=(0,8); pair c=(0,0); pair d=(15,0); dot(a); dot(b); dot(c); dot(d); draw(b--c--d--a--b--d); label("$A$",a, NE); label("$B$",b, NW); label("$C$",c, SW); label("$D$",d, SE); label("9",(a+b)/2,N); label("15",(c+d)/2,S); draw(b/8--b/8+d/15--d/15); draw(b+(a-b)/9--b+(a-b)/9+(c-b)/8-- b+(c-b)/8); [/asy]