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NDA 2019 Maths · Mathematics · Straight Lines · easy

Two parallel sides of a rectangular plot lie along the lines 5x-12y+7=0 and 5x-12y-19=0. The width of the plot is

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Two parallel sides of a rectangular plot lie along the lines 5x−12y+7=05x-12y+7=0 and 5x−12y−19=05x-12y-19=0. The width of the plot is
  1. A. 2626 units
  2. B. 22 units
  3. C. 1213\frac{12}{13} units
  4. D. 11 unit
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Answer: (B) 22 units

For parallel lines ax+by+c1=0ax+by+c_1=0 and ax+by+c2=0ax+by+c_2=0 the distance is ∣c1−c2∣a2+b2=∣7−(−19)∣25+144=2613=2\frac{|c_1-c_2|}{\sqrt{a^2+b^2}}=\frac{|7-(-19)|}{\sqrt{25+144}}=\frac{26}{13}=2. The trap is to leave the denominator as a2+b2=169a^2+b^2=169 or to forget to divide, giving 2626. Both equations already have the same coefficients of xx and yy, so no rescaling is needed.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake