# If the rectangular faces of a brick have | Quantitative Aptitude – Geometry

## CAT 2019 – Slot -1 - Question 3 - If the rectangular faces of a brick have

Q. 3: 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

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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