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
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
Updated On: Sep 17, 2024
- √3 : 2
- 2 : √5
- 1 : √3
- √2 : √3
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The Correct Option is C
Solution and Explanation
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
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
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