Given below is the conversation between …

Given below is the conversation between Gayatri and a mason. Gayatri : Here are some 90 cm x 90 cm tiles. I want to use them in flooring of our courtyard.' Mason: 'If I use all of these tiles, there will be four more coloumns than rows.' Gayatri: I want to make a square floor.' Mason: 'Either some tiles will be left unsued or 35 additional tiles are required.' Gayatri: 'I do not think 35 additional tiles will be required to make a square courtyard.' Mason: 'Okay, that is possible, but you still have to buy some more.' (i) How many tiles did Gayatri have? (ii) What is the minimum number of tiles she has to purchase to make a square courtyard? (iii) For the minimum number of tiles purchased, what can be the side length (in m) of the square courtyard?

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