Given here are n squares which are inclined and touch each other externally at vertices, and are lined up in a row.The distance between the centers of the first and last square is given.The squares have equal side length.The task is to find the side of each square.
Input :d = 42, n = 4
Output :The side of each square is 9.899
Input :d = 54, n = 7
Output :The side of each square is 6.364
There are n squares each having side of length a and the distance between the first and last squares is equal to d. From the figure, it is clear that they are connected by diagonals. Length of each diagonal is equal to a√2.
For the first and last square, only half of the diagonal is covered under the length d.For rest of the (n-2) squares, the complete diagonal is covered in d. Hence the relation between a and d is as follows:
a/√2 + a/√2 + (n-2)*a√2 = d
=> a√2 + √2na – 2a√2 = d
=> n√2a – a√2 = d
=> a = d/((n-1)*(√2))
Side of the square = distance between centers/((no. of squares-1) * sqrt(2)).
Below is the implementation of the above approach:
The side of each square is 9.89949
Time Complexity : O(1)
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