Answer:
Let l be the length of the longer side and b be the length of the shorter side. Given that the length of the diagonal of the rectangular field is 16 m more than shorter side. Thus, Diagonal \[=16+b\] Since longer side is 14 m more than shorter side, \[\therefore \,\,l=14+b\]. We know, \[{{(Diagonal)}^{2}}={{(Length)}^{2}}+{{(Breadth)}^{2}}\] [By Pythagoras theorem] \[\therefore {{(16+b)}^{2}}={{(14+b)}^{2}}+{{b}^{2}}\] \[256+{{b}^{2}}+32b=196+{{b}^{2}}+28b+{{b}^{2}}\] \[{{b}^{2}}-4b-60=0\] \[{{b}^{2}}-10b+6b-60=0\] \[b(b-10)+6(b-10)=0\] \[(b+6)(b-10)=0\] \[\Rightarrow b=-6\] or \[+10\] As breadth cannot be negative \[\therefore \] Breadth \[(b)=10\text{ }m\]. Now, length of rectangular field \[=(14+b)\text{ }m\] \[=(14+10)\text{ }m\] \[=24\text{ }m\] Thus, length of rectangular field is \[24\text{ }cm\] and breadth is 10 m.
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