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  • In Fig. 9.5, if parallelogram ABCD and rectangle ABEM are of equal area, then :(A) Perimeter of ABCD = Perimeter of ABEM (B) Perimeter of ABCD < Perimeter of ABEM (C) Perimeter of ABCD > Perimeter of ABEM (D) Perimeter of ABCD = (Perimeter of ABEM)

In Fig. 9.5, if parallelogram ABCD and rectangle ABEM are of equal area, then :

(A) Perimeter of ABCD = Perimeter of ABEM
(B) Perimeter of ABCD < Perimeter of ABEM
(C) Perimeter of ABCD > Perimeter of ABEM
(D) Perimeter of ABCD = (Perimeter of ABEM)

Answers (1)

best_answer

Answer: [C]

Solution.
 

In a rectangle opposite sides are equal.
  So in ABEM,
AB = EM … (1)
In a parallelogram also the opposite sides are equal.
So in ABCD,
CD = AB   …(2)
Adding eq. (1) and (2)
We get AB + CD = EM + AB
So, CD = EM …(3)
We know that, the shortest distance between any two parallel lines is the perpendicular distance between them. So, perpendicular distance between two parallel sides of a parallelogram is always less than the length of the other parallel sides.
BE < BC and AM < AD
On adding these inequalities, we get
BE + AM < BC + AD
or
BC + AD > BE + AM
On adding AB + CD on both sides, we get
AB + CD + BC + AD > AB + CD + BE + AM
\Rightarrow AB + BC + CD + AD > AB + CD + BE + AM (rearranging LHS)
\Rightarrow AB + BC + CD + AD > AB + BE + EM + AM [Q CD = EM (from eq. 3)]
\Rightarrow Perimeter of ABCD> Perimeter of ABEM
Therefore option (C) is correct.

 

 

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