Ahil grows radishes in his backyard which is in the shape of a square. Each radish takes 1 cm² in his backyard. This year, he has been able to grow 131 more radishes than last year. The shape of the backyard remained a square. How many radishes did Ahil produce this year? (Answer in Integer)
Answers
Given : Ahil grows radishes in his backyard which is in the shape of a square. Each radish takes 1 cm² in his backyard.
This year, he has been able to grow 131 more radishes than last year.
The shape of the backyard remained a square.
To Find : How many radishes did Ahil produce this year?
Solution:
Let say last year ahil grown = n² ( n is the side of square shape of backyard )
This year ahil grown = n² + 131
as shape of the backyard remained a square.
hence n² + 131 is a square
and n² + 131 = ( n + k)² where k is integer
=> n² + 131 = n² + k² + 2nk
=> 131 = k ( k + 2n)
as 131 is prime number
Hence k must be 1
=> 131 = 1 * ( 1 + 2n)
=> 130 = 2n
=> n = 65
Last year grown = 65² = 4225
This year grown = 4225 + 131 = 4356 = 66²
Ahil produce this year 4356 = 66² radishes
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