Q17 of 99 Page 264

The length of diagonal of a rectangular land is 15 meter and the difference of length and breadth is 3 meter. Let us calculate perimeter and area.

Diagonal = 15m, Length - Breadth = 3m

From Pythagorean theorem,


Length2 + Breadth2 = Diagonal2


As, Length = Breadth + 3


Let Length = B + 3, Breadth = B and Diagonal = 15 m


(B + 3)2 + B2 = 152


2B2 + 6B - 216 = 0


Or, B2 + 3B - 108 = 0


B2 + 12B - 9B - 108 = 0


B(B + 12) - 9(B + 12) = 0


Breadth cannot be negative, so B = 9m


Length = 12m


Perimeter = 2(L + B) = 42m


Area = L × B = 108m2


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