During a polar expedition, each member must walk on very soft snow that can withstand a maximum pressure of 4 kPa before it gives way. A fully equipped explorer has a weight of 700 N. The area of the sole of one boot is 225 cm².
(i) Calculate the pressure exerted on the snow by one boot when no additional plate is attached.
(ii) Show that this pressure exceeds the safe limit of the snow.
(iii) To avoid sinking, light rectangular aluminium plates will be fixed under each boot. Determine the minimum additional area that one plate must provide so that the pressure on the snow does not exceed 4 kPa.
(iv) If each aluminium plate is to be square, find the least possible length of its side, in centimetres, correct to the nearest centimetre.