A rectangular floor area can be completely tiled with \(200\) square tiles. If the side length of each tile is increased by \(1\) unit, it would take only \(128\) tiles to cover the floor.
(i) Assuming the original length of each side of a tile be \(x\) units, make a quadratic equation from the above information.
(ii) Write the corresponding quadratic equation in standard form.
(iii) (a) Find the value of \(x\), the length of side of a tile by factorisation.
(b) Solve the quadratic equation for \(x\), using quadratic formula.
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