A rectangular tile has length \(4 x \mathrm {~cm}\) and width \(( x + 3 ) \mathrm { cm }\). The area of the rectangle is less than \(112 \mathrm {~cm} ^ { 2 }\). By writing down and solving an inequality, determine the set of possible values of \(x\).
A second rectangular tile of length \(4 y \mathrm {~cm}\) and width \(( y + 3 ) \mathrm { cm }\) has a rectangle of length \(2 y \mathrm {~cm}\) and width \(y \mathrm {~cm}\) removed from one corner as shown in the diagram.
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Given that the perimeter of this tile is between 20 cm and 54 cm , determine the set of possible values of \(y\).