If the second tallest building is half as tall as the first one's height of 100 feet, it is 100/2= <<100/2=50>>50 feet tall.
If the third tallest building is half as tall as the second one's height of 50 feet, it is 50/2= <<50/2=25>>25 feet tall.
If the fourth building is one-fifth as tall as the third one, it is 25/5= <<25/5=5>>5 feet tall.
Therefore, all four buildings put together would be 100+50+25+5= <<100+50+25+5=180>>180 feet tall.
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