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CAT 2018 [SLOT 2] Quant Question with Solution 31

Question:
A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is

  1. 4 units
  2. 8 units
  3. 4√2 units
  4. 2√2 units
Show Answer
Correct Answer: 1

Since we want point A to be as close to the origin as possible, let point A lie on the x axis and its coordinates be (a, 0).
The distance of A from side BC (lying on the line x = 4) is the height of the triangle
=> The height of the triangle ABC = |a – 4|
Given the area of the triangle = 32
=> (1/2) × 8 × |a – 4| = 32 => |a – 4| = 8
=> a = 12 or –4
Required answer is the shortest distance from (0, 0) i.e. 4 when a = –4.

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