Question 58

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

Solution

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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