A British Thermal Unit (BTU) is equal to the amount of energy used to raise the temperature of one pound of water 1°F. A house is shaped like a rectangular prism with a length, width, and height of 80 feet, 25 feet, and 8 feet, respectively. Approximately 60,000 BTUs are required to heat the house properly. ​​a. What is the density of the house in BTUs?
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​​b. A nearby house requires approximately 52,000 BTUs for heating. If the house is 31 feet long and 25 feet wide, what is the height of the house? Round your answer to the nearest foot.