What is the area of ​​the largest possible rhombus that can be inscribed in a rectangle?

The rhombus inscribed in a rectangle is tangent to the sides of the rectangle, so we can infer that the diagonal of the largest inscribed rhombus is equal to the length and width of the rectangle.

If we have the length (l) and width (b) of the rectangle, the diagonal lengths of the largest inscribed rhombus are d1 = l and d2 = b.

The area of ​​a rhombus is given by the formula,

Area = (d1*d2)/2

Substituting the values ​​of d1 and d2, we get:

Area = (l*b)/2

Using this formula, we can create a calculation Program that can inscribe the area of ​​the largest rhombus within a rectangle,

Example

Real-time demonstration

#include <stdio.h>
int main() {
   float l = 16, b = 6;
   float area = (l*b)/2;
   printf("The area of rhombus inscribed in a rectangle of length %f and breadth %f is %f", l,b,area);
   return 0;
}

Output

The area of rhombus inscribed in a rectangle of length 15 and breadth 12 is 90.

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