Given the area of three faces of the rectangular parallelepiped which has a common vertex. Our task is to find the sum of lengths of all 12 edges of this parallelepiped.
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. By analogy, it relates to a parallelogram just as a cube relates to a square or as a cuboid to a rectangle. A picture of a rectangular parallelepiped is shown below.
Input: 1 1 1 Output: 12 Input: 20 10 50 Output: 68
Approach: The area given are s1, s2 and s3 . Let a, b and c be the lengths of the sides that have one common vertex. Where , , . It’s easy to find the length in terms of faces areas: , , . The answer will be the summation of all the 4 sides, there are four sides that have lengths equal to a, b and c.
In the first example the given area s1 = 1, s2 = 1 and s3 = 1. So with the above approach, the value of a, b, c will come out to be 1. So the sum of the length of all 12 edges will be 4 * 3 = 12.
Below is the implementation of the above approach:
- Split the array into odd number of segments of odd lengths
- Reach the numbers by making jumps of two given lengths
- Rectangular (or Pronic) Numbers
- Maximum of smallest possible area that can get with exactly k cut of given rectangular
- Number of Simple Graph with N Vertices and M Edges
- Minimum number of square tiles required to fill the rectangular floor
- Program to find total number of edges in a Complete Graph
- Find middle point segment from given segment lengths
- Minimum edges to be added in a directed graph so that any node can be reachable from a given node
- Find the number of distinct pairs of vertices which have a distance of exactly k in a tree
- XOR of a submatrix queries
- Sum of the natural numbers (up to N) whose modulo with K yield R
- Find whether only two parallel lines contain all coordinates points or not
- Longest sub-sequence of array containing Lucas numbers
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.