Answer :

Let the length and breadth of the rectangle be l and b respectively


Perimeter of a rectangle is 82 m


2(l + b) = 82


l + b = 41


l = 41 - b - - - - - - (1)


Area is 400 m2


lb = 400


(41 - b) b = 400 using (1)


41b –b2 = 400


b2 - 41b + 400 = 0


Using the splitting middle term - the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = - 41 c = 400


= 1.400 = 400


And either of their sum or difference = b


= - 41


Thus the two terms are - 25 and - 16


Difference = - 25 - 16 = - 41


Product = - 25. - 16 = 400


b2 - 25b - 16b + 400 = 0


b(b - 25) - 16(b - 25) = 0


(b - 25) (b - 16) = 0


b = 25 or b = 16


If b = 25 l = 41 - 25 = 16 but l cannot be less than b


Thus b = 16m


The breadth of the rectangle = 16m

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