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The perimeter of a parallelogram whose sides are represented by the lines x + 2 y + 3 = 0 , 3 x + 4 y - 5 = 0 , 2 x + 4 y + 5 = 0 and 3 x + 4 y - 10 = 0 is equal to

Options

  1. A5 2 + 5 5 units
  2. B5 + 5 5 units
  3. C5 + 5 2 5 units
  4. D5 + 5 5 2 units

Correct answer

A. 5 2 + 5 5 units

Step-by-step solution

Let, the parallelogram is A B C D as shown in the figure. Let, the distance between A B & C D is d 1 and the distance between A D & B C is d 2 and ∠ D A B = ∠ D C B = θ then, A D = d 1 c o s e c θ and D C = d 2 c o s e c θ ⇒ Perimeter of the parallelogram A B C D is 2 A D + D C = 2 c o s e c θ d 1 + d 2 Now, d 1 = - 3 2 + 5 4 1 + 1 4 = 1 2 5 & d 2 = 5 2 - 5 4 1 + 9 16 = 1 and tan ⁡ θ = - 1 2 + 3 4 1 + 3 8 = 2 11 or cot ⁡ θ = 11 2 or c o s e c θ = 1 +

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