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)
- Find the side of the squares which are lined in a row, and distance between the centers of first and last square is given
- Find the Side of the smallest Square that can contain given 4 Big Squares
- Count squares with odd side length in Chessboard
- Number of squares of side length required to cover an N*M rectangle
- Find the radii of the circles which are lined in a row, and distance between the centers of first and last circle is given
- Program to find third side of triangle using law of cosines
- Find coordinates of the triangle given midpoint of each side
- Program to find the side of the Octagon inscribed within the square
- Diagonally Dominant Matrix
- Find a point that lies inside exactly K given squares
- Puzzle | Program to find number of squares in a chessboard
- Find the number of squares inside the given square grid
- Length of the chord the circle if length of the another chord which is equally inclined through the diameter is given
- Check whether two points (x1, y1) and (x2, y2) lie on same side of a given line or not
- Minimum and maximum possible length of the third side of a triangle
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.