The length of each side of the original square is 4 m
A square each side x is transformed into a rectangle by increasing the length by 8 m. Thus, new length = x + 8
The new width increases by 5 m will be;
New width = x + 5
If the area of the resulting rectangle is 108 m², then we have;
(x + 5)(x + 8) = 108
x² + 13x + 40 = 108
x² + 13x - 68 = 0
x² + 17x - 4x - 68 = 0
x(x + 17) - 4(x + 17) = 0
(x + 17)(x - 4) = 0
x = 4 or -17
ignore negative
So side of square = 4 m
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