A farmer owns a perfectly square field and plans to install a strong fence along its entire boundary to protect crops from animal. The total length of fencing available is \(460\ meters\). In addition, he dreams of planning a large tree exactly at the centre of the field to provide shade and beauty. To carry out his plan, he needs to calculate the field's side length and area accurately.
(i) The length of each side of the field _______\(m\)
(ii) Obtain the area of the field in square meters?
(iii) If square tree grid with an area of \(150\ m^2\) in the centre of the field, identify the side length of this grid to the closest whole meter.
(iv) if the farmer plans to plant \(2025\) plants such that number of rows equals the number of plants per row, how many plants are in each row? (Use prime factorisation)