Longest edge ?

Geometry Level 1

The length of three unequal edges of a rectangular solid block are in G.P. The volume of the block is $216 cm^{3}$ and the total surface area is $252 cm^{2}$ . The length of the longest edge is

18 cm 6 cm 12 cm 3 cm

2 solutions

Mustafa Rokadiya
Mar 6, 2014

volume =216 =>l b h=216; l,b,h are in G.P. => b b=l h => b b b=216 => b=6; Now, surface area=252 => 2(lb+bh+hl) = 252; => 2(6l + 6h + 36) = 252 =>l+h=15. Now, longest edge length can't be 3 as b=6. It can't be 6 as l+h =15. nor it can be 18. So, last possible answer is 12.

Let the dimensions be a/r, a, ar. Volume = a^3=216, a=6, S.A.=2(a a/r+a^a^2 r+a^2)=252. Solve it and r will be equal to 2 hence you can easily find the dimensions:)

Kushagra Sahni - 7 years, 3 months ago

Rohan Kumar
Mar 8, 2014

its so easy just find three terms in GP whose product equal to 216 you get 2 sets 3,6,12 and 2,6,18 you willl find that the set 3,6,12 will satisfy the surface area equal to 252 therefore the longest side will be 12

Longest edge ?

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