Question

If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively.Calculate the area
of the rectangular fiel(d)
(a) 25 cm2
(b) 29 cm2
(c) 18 cm2
(d) 20 cm2

Answer 1

let l be the length and b be the breadth of rectangular field .

Given , perimeter of rectangle = 18 cm

2 ( l + b ) = 18 cm

l + b = 18 / 2 = 9 cm

l + b = 9 cm

Given ,

diagonal of rectangle = √41 cm

since , we know that
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diagonal of rectangle

=√[( length )^2 + ( breadth )^2 ]
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√( l^2 + b^2) = √41

l^2 + b^2 = ( √41 )^2

l^2 + b^2 = 41

l^2 + b^2 + 2 lb - 2 lb = 41

( l + b )^2 - 2 lb = 41

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since , we have l + b = 9 , so now
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( 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 cm^2

l × b = 20 cm^2

length × breadth = 20 cm^2

therefore ,

area of rectangular field = 20 cm^2

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Your Answer : option (d ) 20 cm^2
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