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 \(45\).