question_answer

The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side, then find the lengths of the sides of the field.

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.