If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively.Calculate the area of the rectangular field ?

Perimeter of rectangle = 18 cm
2 ( l + b ) = 18 cm
l + b = 18 / 2
= 9 cm
l + b = 9 cm

Diagonal of rectangle = √41 cm
We know that, Diagonal of rectangle = √ [ ( length )² + ( breadth )² ] √( l² + b²) = √41
l² + b² = ( √41 )²
l² + b² = 41
l² + b² + 2 lb – 2 lb = 41
( l + b )² – 2 lb = 41

Since , we have l + b = 9 , so now
( 9 )² – 2 l b = 41
81 – 2 lb = 41
2 lb = 81 – 41
2 lb = 40
lb = 40 / 2 = 20 cm ²
l × b = 20 cm²
Therefore, area of rectangular field = 20 cm²