If 3x - 4y - 5 = 0 and 3x - 4y + 15 = 0 are the equations of a pair of opposite sides of a square, then what is the area of the square?

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NDA (Held On: 6 Sep 2020) Maths Previous Year paper
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  1. 4 square units
  2. 9 square units
  3. 16 square units
  4. 25 square units

Answer (Detailed Solution Below)

Option 3 : 16 square units
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Detailed Solution

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Concept:

The distance between the lines ax + by + c1 = 0 and ax + by + c2 = 0  is 

Area of square = (side)2 

 

Calculation:

Here, 3x - 4y - 5 = 0 and 3x - 4y + 15 = 0 are the equations of a pair of opposite sides of a square.

Distance between them =

 

Now area of square = 42 sq. units 

= 16 sq. units 

Hence, option (3) is correct.

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