Sue the T-Rex grows cabbage in a square shaped garden. Each cabbage takes #1 ft^2# of area in the garden. This year, she increased her output by 211 cabbages compared to last year, If the shape remains a square how many cabbages did she grow this year?

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Answer 1 · 2016-05-18T06:51:16

Sue the T-Rex grew #11236# cabbages this year.

Squares of numbers follow the series #{1,4,9,16,25,36,49,......}#

and difference between consecutive squares is the series

#{1,3,5,7,9,11,13,15,.......}# i.e. each term #(2n+1)# times the previous one.

Hence if output has increased by #211=2*105+1#, it should be #105^2# last year i.e. #11025# last year and #11236# this year, which is #106^2#.

Hence, she grew #11236# cabbages this year.