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

Let the no. of rows = x

no. of plans in each row = x

Total number of plants = no. of rows × no. of plants in each row

                                     = x^2

given that, total number of plants = 2025

⇒x^2=2025

⇒ x=root 2025

⇒ x = 45

No. of rows = 45

No. of plants in each row = 45 

Answer 2

Let the number of rows be ⇒  x.

The number of plants in each rows would be = x.  

Number of plants in total = x²

Here x² = 2025

To find x we need to find the square root of 2025. So here I am going to use prime factorization method.

$\begin{array}{r | l} 3 & 2025\\ \cline{2-2} 3 & 675 \\ \cline{2-2} 3 & 225 \\ \cline{2-2} 3 & 75 \\\cline{2-2} 5 & 25 \\\cline{2-2} & 5 \\ \end{array}$

2025 = 3×3×3×3×5×5

√2025 = 3×3×5 = 45

∴ x = 45

∴Number of rows = 45

∴Number of plants in each row = 45