Answer :

Given.


Perimeter = 42 m


Diagonal = 15 m


Formula used/Theory


Pythagoras theorem:-


Base2 + Height2 = Hypotenuse2


Perimeter of rectangle = 2(L + B)


If Perimeter of rectangle = 2(L + B)


Then;


2(L + B) = 42m


(L + B) =


(L + B) = 21m


Let L be x


Then, B is (21–x)


Then by Pythagoras theorem:-


Base2 + Height2 = Hypotenuse2


x2 + (21–x)2 = 152


x2 + (21)2 + x2–2×x× 21 = 225


2x2 – 42x + (441 – 225) = 0


2x2 – 42x + 216 = 0


2(x2 – 21x + 108) = 0


x2 – 21x + 108 = 0


As comparing eq to ax2 + bx + c = 0


x = = 12


x = = 9


if length is 12m


then, breadth = (21–12) = 9m


if length is 9m


then, breadth = (21–9) = 12m


Conclusion/Result.


Length of sides can be either (12,9) or (9,12)


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