The altitude's slope must be perpendicular to that of the line.
The slope of segment BC is 2/5. The slope of the altitude must be perpendicular to 2/5. Since the negative reciprocal of 2/5 is -5/2, then the slope of the altitude is -5/2.
It depends if 24cm is the long dimension or the short one...it's the answer if 24cm is the short dim. if 24cm is the long dimension then the answer is 24/1.618