Q165 / 270 · NDA 2020 · Mathematics

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

  • A
    4 square units
  • B
    9 square units
  • Correct answer
    C
    16 square units
  • D
    25 square units

Solution

We know that pair of opposite sides of my square are parallel. So, distance between two parallel sides $=$ Side length of the square $\therefore$ Side length of the square $=\left|\frac{15-(-5)}{\sqrt{3^2+4^2}}\right|=\frac{20}{5}=4 \text { units }$ Area of the square $=4 \times 4=16$ units square.

Hence, the correct answer is option: 'C'.

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