Question 1125600
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            This problem admits easy MENTAL solution.



<pre>
Since the perimeter is 28 units, the sum of the length and the width is half ot it, i.e. 14 units.


Hence, the average of the length and the width is half of 14, i.e. 7 units.


The average is equally remoted value from the length and the width, i.e.


    L = 7 + u,  W = 7 - u,


where "u" is that common distance.


Then  the area  45 = L*W = (7+u)*(7-u) = 49 - u^2,   which means  


                u^2 = 49 - 45 = 4   and  hence   u = {{{sqrt(4)}}} = 2 units.


Then  L = 7 + 2 = 9  and  W = 7 - 2 = 5.


Then the diagonal is  {{{sqrt(9^2 + 5^2)}}} = {{{sqrt(81+25)}}} = {{{sqrt(106)}}}.
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Solved.