Maximum area of a Rectangle that can be circumscribed about a given Rectangle of size LxW
Given a rectangle of dimensions L and W. The task is to find the maximum area of a rectangle that can be circumscribed about a given rectangle with dimensions L and W.
Input: L = 10, W = 10
Input: L = 18, W = 12
Approach: Let below is the given rectangle EFGH of dimensions L and W. We have to find the area of rectangle ABCD which is circumscribing rectangle EFGH.
In the above figure:
If then as GCF is right angled triangle.
Now, The area of rectangle ABCD is given by:
Area = AB * AD
Area = (AE + EB)*(AH + HD) …..(1)
According to the projection rule:
AE = L*sin(X)
EB = W*cos(X)
AH = L*cos(X)
HD = W*sin(X)
Substituting the value of the above projections in equation (1) we have:
Now to maximize the area, the value of sin(2X) must be maximum i.e., 1.
Therefore after substituting sin(2X) as 1 we have,
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)