Quantitative Aptitude – Geometry


Slot – 1 – Quantitative Aptitude – Geometry – If the rectangular faces of a brick have

Q. If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is?
  1. 2 : √5
  2. 1 : √3
  3. √2 : √3
  4. √3 : 2
Answer: 1 : √3

Solution: Let the size of bricks are l*b*h such that l > b> h
As we know diagonals = (l^2 + b^2 )^1/2 , (l^2 + h^2 )^1/2 , and (h^2 + b^2 )^1/2
Thus ratio of squares of diagonals = (l^2 + b^2 ) : (l^2 + h^2) : (h^2 + b^2 ) = (√15)^2 : (2√3)^2 : 3^2
Or (l^2 + b^2 ) : (l^2 + h^2) : (h^2 + b^2 ) = 15 : 12 : 9 = ( 9 + 6) : (9 + 3) : (3 + 6)
By comparing we can say l^2 = 9, h^2 = 3 and b^2 = 6
So l = 3 and h = √3
Required ratio of h/l = √3/3 = 1: √3

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