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784 = 2 × 2 × 2 × 2 × 7 × 7

Since perimeter of the base is 30 cm, this means the sum of the length and width is 15 cm.

Looking at the prime factors above, the only way we can make 15 cm is by adding “2 × 2 × 2″ and “7”.

Rearranging the factors, it becomes:

= (2 × 2 × 2) × 7 × (2 × 7)
= 8 × 7 × 14

Since the length and width are 8 cm and 7 cm, this means the height must be 14 cm.

 

 

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