In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Q: Problem: 12 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? 
Options: a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45

A: a
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Q: Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 20 : 60 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ? 
Options: a ) 1200 , b ) 1250 , c ) 1300 , d ) 1400 , e ) 1450

A: a
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Q: Problem: what is the perimeter of a square field whose diagonal is 8 √ 2 ? 
Options: a ) 82 m , b ) 32 m , c ) 27 m , d ) 26 m , e ) 76 m

A:
b
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