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
- 4 units
- 8 units
- 4√2 units
- 2√2 units
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.
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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