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



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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