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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 312 cm^2. The length of the longest edge is ?

 Jul 30, 2021
 #1
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The longest edge = 18 cm

 

2, 6, 18

 Jul 30, 2021
edited by Guest  Jul 30, 2021
 #2
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Side lengths are x    xr     and   xr^2

 

x * x^r * xr^2 = 216

 

x^3 r^3 = 216

xr = 6      and     6/r = x

and    

2 (x*xr) + 2 (xr*xr^2) + 2 ( xr^2 * x) = 312

12x          + 12xr^2    +   2 x^2 r^2

72/r          + 72 r         +   72  = 312

72            + 72 r^2      + 72r   = 312 r

72r^2   - 240 r  + 72  = 0 

 

 

 

    Quadratic Formula shows r = 3           then x = 2        xr = 6     xr^2 = 18 cm

 Jul 30, 2021

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