How the heck.

(XY / PQ)²   =   area of UVWXY / area of LMNPQ

 

(XY / 10)²   =   198 / 88

 

(XY / 10)²   =   9 / 4

 

XY / 10   =   √[ 9 / 4 ]

 

XY / 10   =   3 / 2

 

XY   =   10 * 3 / 2

 

XY   =   30 / 2

 

XY   =   15

198/88=2.25 

so 10*2.25=22.5