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Question

2025plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.


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Solution

Given that,

The number of plants in a garden are 2025.

Let's assume the number of rows in a garden be,R

So, each row has a number of plants R

Therefore, total number of plants = R × R

That indicates R × R = 2025

The prime factorization of 2025 is shown below,

R × R = 2025

R2 = (3×3)×(3×3)×(5×5)

R2 =(3×3×5)×(3×3×5)

R2 = 45×45

R = (45×45)

R = 45

Therefore, the number of rows, R = 45

The number of plants in each row, R = 45 .

Hence, the number of rows is 45 and the number of plants in each row is 45.


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