Q. 265.0( 2 Votes )

The lengths of th A. 12 cm

B. 6 cm

C. 18 cm

D. 3 cm

Answer :

Given that:

Volume of a block = 216cm3


and Total Surface area = 252 cm3



Breadth of a rectangular block = a


& Height of a rectangular block = ar


Since, they are in G.P so there common ratio is same.


and we know that,


Volume of a rectangular solid block = L × B × H


[given]


216 = a3



a = 6 …(i)


Now,


Total Surface Area of a block = 2[L×B + B×H + H×L]


[given]



[from (i)]





2(r2 + r + 1) = 7r


2r2 + 2r + 2 – 7r = 0


2r2 – 5r + 2 = 0


2r2 – 4r – r + 2 = 0


2r(r – 2) – 1(r – 2)= 0


(2r – 1)(r – 2) = 0


2r – 1 = 0 & r – 2 = 0


and r = 2


Three unequal edges of the given solid block are:


Case 1: If a = 6 and r = 2, then



Breadth = a = 6


and Height = ar = 6 × 2 = 12


Case 2:



Breadth = a = 6


and


So, the length of the longest side = 12units


Hence, the correct option is (a)

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