...

y = 22 - x

Sub into the other equation

x (22 - x) = 117
22x - x2 = 117
x2 - 22x + 117 = 0
(x - 13) (x - 9) = 0
x = 13, x = 9

Sub into y = 22 - x

y = 9, y = 13

So the rectangle is 13 cm by 9 cm long i.e. the shorter side is 9 cm long

This question should not be seen in Sec 2 work. Sec 2 work only covers simultaneous linear equations in two variables and obviously xy = 117 is not linear. This is more of a Sec 3 A Maths question than a Sec 2 Maths question.