Question
Quantitative Aptitude Question on Mensuration
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
A
4units
B
8units
C
4√2units
D
2√2units
Answer
4units
Explanation
Solution
The correct answer is (A):
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.