Question

$2025$plants 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.

Answer 1

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 $=$ $R$ $\times$ $R$

That indicates $R$ $\times$ $R$ $=$ $2025$

The prime factorization of $2025$ is shown below,

$R$ $\times$ $R$ $=$ $2025$

$R^2$ $=$ $(3\times 3)\times (3\times 3)\times (5\times 5)$

$R^2$ $=$$(3\times 3\times 5)\times (3\times 3\times 5)$

$R^2$ $=$ $45\times 45$

$R$ $=$ $\sqrt{(45\times 45)}$

$R$ $=$ $45$

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 $45$.