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 ?
+37159 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
