a farmer grows broccoli in his farm that is in the shape of a square . each broccoli takes 1 square foot of area in his garden . this year , he has increased his output by 101 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did he produce this year ?
explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 101 , the area would have increased by 101 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 101 ( x + y ) ( x - y ) = 101 . 101 is a prime number and hence it will have only two factors . i . e . , 101 and 1 . therefore , 101 can be expressed as product of 2 numbers in only way = 101 * 1 i . e . , ( x + y ) ( x - y ) = 101 * 1 so , ( x + y ) should be 101 and ( x - y ) should be 1 . solving the two equations we get x = 51 and y = 50 . therefore , number of broccoli produced this year = x 2 = 512 = 2601 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , c and d . as 2400,1987 and 2000 are not the square of any number . check choice b : if this year ' s produce is 2601 , last year ' s produce would have been 2601 - 101 = 2500 2500 is the square of 50 . so , 2601 is the answer . choice b
power(divide(add(101, 1), const_2), const_2)