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14 Jun 2019, 11:07
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:53) correct
31%
(01:59)
wrong
based on 55
sessions
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Not Attempted Yet
In a rhombus, the ratio of length of side to the length of smaller diagonal is 5 : 6, then find the ratio of the length of smaller diagonal to that of the larger diagonal.
A. 1:3
B. 1:2
C. 2:3
D. 3:5
E. 3:4
A. 1:3
B. 1:2
C. 2:3
D. 3:5
E. 3:4
Chethan92
Joined: 18 Jul 2018
Last visit: 21 Apr 2022
Posts: 899
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Given Kudos: 95
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy)
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14 Jun 2019, 11:19
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From the attached file, we can see that the side of rhombus and the smaller diagonal form the hypotenuse and base of a right-angled triangle.
The height of the triangle will be 4x.
LARGEST DIAGONAL = 2*4x = 8x
Ratio = 6x:8x = 3:4
E is the answer.
The height of the triangle will be 4x.
LARGEST DIAGONAL = 2*4x = 8x
Ratio = 6x:8x = 3:4
E is the answer.
Attachments
Rhombus.png [ 5.45 KiB | Viewed 3398 times ]
14 Jun 2019, 11:23
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nick1816
Let length of each side = a
Length of small diag = d
And length of larger diag = D
Property of Rhombus —> It makes 4 right angle triangles with half of each diagonals and each side as hypotenuse
—> a^2 = (d/2)^2 + (D/2)^2
—> 4*a^2 = d^2 + D^2
Given, the ratio of length of side to the length of smaller diagonal is 5 : 6
—> a:d = 5:6
Or a = 5k and d = 6k, where k is any constant
—> 4*(5k)^2 = (6k)^2 + D^2
—> D^2 = 64*k^2
—> D = 8k
So, ratio of d : D = 6k : 8k = 3:4
IMO Option E
Pls Hit kudos if you like the solution
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