In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
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Question: Problem: in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz 
Options: a ) 1.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm

Answer: a


Question: Problem: how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ? 
Options: a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140

Answer: a


Question: Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ? 
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24

Answer:
e