Consider a cuboid all of whose edges are integers and whose base is square. Suppose the sum of all its edges is numerically equal to the sum of the areas of alll its six faces. Then the sum of all its edges is.

Options

A. 12
B. 18
C. 24
D. 36

Answer

c

Explanation

Let sides are a,a,h
`So, 4a+4h+4a=2(a^(2)+ah+ah)`
`Rightarrow a^(2)-4a=2h(1-a)`
`(a^(2)-1)+1-4(a-1)-4=2h(1-a)`
`(a-1) (a+1)-4 (a-1)-3=2h(1-a)`
`Rightarrow2h= 3/(a-1)+4-(a+1)`
Soa=2 & h=2 are the only integral solution (a & h are positive integers).