Question

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 1

Answer:

4356 radishes

Step-by-step explanation:

1cm square=1 radish

let x=new year and y=past year

x square-y square=131

(x-y) (x+y) =131*1

x+y=131- 1 st eqn

x-y=1- 2nd eqn

by adding eqn 1 and eqn 2

we get 2x=132

so x=66

so no of radishes=66 square

                            =4356 radishes

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Answer 2

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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