Step 1: Understanding the symptoms.
The combination of low BMR (basal metabolic rate), delayed puberty, and mental retardation is indicative of a disease related to thyroid function. One such disease is "hypothyroidism," a condition in which the thyroid gland does not produce enough thyroid hormones.
Step 2: Conclusion.
The disease associated with low BMR, delayed puberty, and mental retardation is "hypothyroidism."