Question

three cubes of metal whose edges are in the ratio 3 ratio 4 is 5 or metal down into a single cube whose diagonal is 12 under root 3 cm find the edge of the three cubes​

Answer 1

Let the sides of the cubes be 3x, 4x and 5x respectively and the side of the new cube be a.

Since volume of new cube = sum of the volume of the thee cubes

                                   a^3 = (3x)^3 + (4x)^3 +(5x)^3

                                  a^3 = (27 + 64 + 125) X x^3

                                  a^3 = 216x^3

                          Therefore, a = 6x

The diagonal of a cube is a√3

Therefore, 6x√3 = 12√3

               6x = 12

               x = 2

Finally the sides of the three cubes are 6cm, 8cm and 10cm

Hope it is helpful to you