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: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .
Options: ['a ) 180 cm', 'b ) 220 cm', 'c ) 240 cm', 'd ) 270 cm', 'e ) 300 cm']
[A]: c

[Q]: Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 70 sq . cm . find the length of the rectangle .
Options: a ) 12 cm , b ) 14 cm , c ) 16 cm , d ) 18 cm , e ) 20 cm
[A]: d

[Q]: Problem: consider a square of diagonal length d . let another square be formed with d as its side . find the ratio of the area of the bigger square to that of the smaller square .
Options: ['a ) 2', 'b ) 3', 'c ) 4', 'd ) 16', 'e ) 41']
[A]:
a