Question 972505
(Make a drawing of the situation to more easily analyze the problem.)


Let dimensions of yard be x and y, and 18 be part of the x and 51 be part of the y of the garden.


Yard Area,  {{{xy}}}
Garden Area, {{{18*51}}}.
Yard Area not containing garden,{{{(x-18)(y-51)}}}.


Ambiguous:  Either "whole back end" is x=18  or it is y=51.


{{{(x-18)(y-51)}}}, the reduced back yard area, 24% of total yard area.
{{{highlight((x-18)(y-51)=0.24(xy))}}}.


That ambiguous part can be used to decide which way x or y should be assigned.  Each choice will give a quadratic equation in either x or y.


(Another exercise not responded with a complete solution; but just a strategy with part of the process.)