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: the length of a rectangle is reduced by 15 % . by what % would the width have to be increased to maintain the original area ? 
Options: ['a ) 10 %', 'b ) 20 %', 'c ) 17.6 %', 'd ) 30 %', 'e ) 35 %']

A: c
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Q: Problem: the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ? 
Options: a ) 128 cm 2 , b ) 36.0 cm 2 , c ) 105 cm 2 , d ) 25 cm 2 , e ) 135 cm 2

A: c
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Q: Problem: 16 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 ) 144 , b ) 131 , c ) 232 , d ) 90 , e ) 45

A:
c
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