Question

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

(a) 12

(b) 18

(c) 24

(d) 36

Answer 1

Answer is : (c) 24

Given, a cuboid has all edges are integers and base is square.

Let the length, breadth and height of cuboid is x, x, y.

Sum of all edges of cuboid = 4x+4x+4y

Sum of area of all faces = 2x²+2xy+2xy

Given, Sum of all edges of cuboid = Sum of area of all faces

x is integer, when y = 2

∴ y = 2, x = 2

Hence, sum of edges = 8x+4y = 16+8 = 24.