1. If the sum of the length, breadth and height of a rectangular parallelopiped is 24 cm and the length of its diagonal is 15 cm then its total surface area is
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By: anil on 05 May 2019 02.25 am
Let the length, breadth and height be $$L,B$$ and $$H$$. The base diagonal, $$P^2=L^2+B^2$$ Again, main diagonal, $$D^2=P^2+H^2$$ => $$L^2+B^2+H^2=(15)^2=225$$ Also, it is given that $$L+B+H=24$$ Total surface area = $$2(LB+BH+HL)=x$$ Using square of three term expression, we get : => $$(L+B+H)^2=(L^2+B^2+H^2)+2(LB+BH+HL)$$ => $$(24)^2=225+x$$ => $$x=576-225=351$$ $$cm^2$$ => Ans - (A)
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