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14 May 2020, 07:34
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
47% (02:27) correct
53%
(02:13)
wrong
based on 43
sessions
History
Date
Time
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Not Attempted Yet
Consider two triangles ABC and ABD with internal angles as shown and a common side AB. What is the length of side AC?
(1) AD^2 + AC^2=1000
(2) CD = 10(√3 + 1)
Attachment:
476627_2d121386-2ad0-497e-ae04-386933531efd_lg.png [ 10.5 KiB | Viewed 1314 times ]
ArunSharma12
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
Posts: 512
Given Kudos: 74
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
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14 May 2020, 08:11
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Bunuel
in triangle ABC: three sides are in the \(1:\sqrt{3}:2\)
BC = x, AB = \(\sqrt{3}x\), AC = 2x
in triangle ADB: BD = AB
BD = \(\sqrt{3}x\)
statement 1:
AD^2 + AC^2=1000
AD^2 = BD^2 + AB^2 = 3x^2 + 3x^2 = 6x^2
AC^2 = BC^2 + AB^2 = 3x^2 + x^2 = 4x^2
6x^2 + 4x^2 = 1000
x^2 = 100
x =10
AC =20
statement 2:
CD = 10(√3 + 1)
CD = BC+ BD = \(x + \sqrt{3}x = x(\sqrt{3} + 1)\)
x = 10
AC = 20
Ans: D
14 May 2020, 09:42
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Bunuel
This is a great question and it hinges on your understanding of right angled triangles.
Always remember:
In a 30-60-90 triangle, the sides are in the ratio: 1:√3:2 ---- (1)
In a 45-45-90 triangle, the sides are in the ratio: 1:1:√2 ---- (2)
We'll make use of this property extensively in this question.
STATEMENT 1: (1) AD^2 + AC^2=1000
Let BC = x (it is opposite to angle of 30 degree)
Then, using (1), we have:
AB = √3x and AC = 2x
Now, in triangle ADB,
AB = √3x, AD = √6x and DB = √3x (using equation (2))
Therefore,
AD^2 + AC^2 = 1000
(√6x)^2 + (2x)^2 = 1000
10x^2 = 1000
x = 10
Through this, we can easily find the value of AC.
Sufficient
STATEMENT 2: (2) CD = 10(√3 + 1)
CD = DB + BC
CD = √3x + x
CD = (√3+1) x = 10(√3+1)
x = 10
Through this, we can easily find the value of AC.
Sufficient
