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 ?
+128474 a = shortest edge
ar = 2nd edge
ar^2 = longest edge
Volume = product of edge lengths....so....
216 = a^3 * r^3 take the cube root of both sides
6 = ar
6/a = r
And for the surface area we have
312 = 2 [ a* ar + a* ar^2 + ar * ar^2 ]
156 = a * 6 + a^2r^2 + a^2 * r^2 * r
156 = 6a + 36 + 36r
120 = 6a + 36 ( 6/a)
20 = a + 36/a
20a = a^2 + 36
a^2 - 20a + 36 = 0
(a - 18) ( a - 2) = 0
The second factor set = 0 gives us what we need for the shortest side = 2
r = 6/a = 6/2 = 3
The longest side = ar * r = 6 * 3 = 18 cm
