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

A. 25 cm2

B. 29 cm2

C. 18 cm2

D. 20 cm2

Answer : D. 20 cm2

Explanation:

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

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