Question

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

• A. √3 : 2
• B. 2 : √5
• C. 1 : √3
• D. √2 : √3

Answer 1

The Correct Option is C

Let's assume the edges of the brick be a,b, and c such that a < b < c
a² + b² = 32 = 9 .... (1)
a² + c² = (2√3)² = 12 .... (2)
b² + c² = (√15)² = 15 .... (3)
By adding all three equations , We get
2(a² + b² + c²) = 9 + 12 + 15 = 36
a² + b² + c² = 18 ..... (4)
From equation (1) and (4) , c = 3;
From equartion (3) and (4) , a = √3
∴ required ratio = a/c = √3/3 = 1/√3