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

It is given that in the garden, each row contains as many plants as the number of rows.
Hence,
$\text{Number of rows} = \text{Number of plants in each row}$
$\text{Total number of plants} = \text{Number of rows} × \text{Number of plants in each row}$
$\text{Number of rows} × \text{Number of plants in each row }= 2025$
$\text{(Number of rows)}^2 = 2025$
$\text{Number of rows} = \sqrt{2025}$
$2025=\underline{5\times5}\times\underline{3\times3}\times\underline{3\times3}$
∴ $\sqrt{2025}=5\times3\times3=45$

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