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Triangle ABC has an area of 9. If AC is three times as long as CB, wha

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Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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New post 09 Oct 2018, 01:57
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A
B
C
D
E

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  15% (low)

Question Stats:

93% (01:31) correct 7% (00:00) wrong based on 15 sessions

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Re: Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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New post 09 Oct 2018, 02:05
Ans is option C 2√15

Bcz ac is 3x

Bc is x

Value of x comes to be √6

Therefore ab comes to be √60

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Re: Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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New post 09 Oct 2018, 02:06
Bunuel wrote:
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Triangle ABC has an area of 9. If AC is three times as long as CB, what is the length of AB?


(A) \(6\)

(B) \(3\sqrt{6}\)

(C) \(2\sqrt{15}\)

(D) \(4\sqrt{15}\)

(E) \(15\)


Attachment:
Capture (2).JPG



AC =X

CB= 3x

Area = 1/2* x*3x


1/2 * x*3x = 9

x = \(\sqrt{6}\)


\(AB^2 =AC^2 +CB^2\)

AB^2 =\((\sqrt{6})^2 *(3\sqrt{6})^2\)

AB=\(\sqrt{60}\)
\(AB = 2\sqrt{15}\)


The best answer is C.
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Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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New post 09 Oct 2018, 02:13
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In the triangle ABC, if the length of side CB is \(x\), the length of the side AC is \(3x\). (From the question stem)

Since this is a right-angled triangle, the length of AB(hypotenuse) is \(\sqrt{(3x)^2 + x^2} = \sqrt{10x^2}\)

We are told that the area of the triangle ABC is 9. Now, \(\frac{1}{2}*x*3x = 9\) -> \(3x^2 = 18\) -> \(x = \sqrt{6}\)

Therefore, the length of AB is \(\sqrt{10x^2}\) which is \(\sqrt{60}\) or \(2\sqrt{15}\)(Option C)

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Re: Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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New post 09 Oct 2018, 02:14
Let bc = x, so ac=3x
We know that,
Area of traigle = 1/2*bc*ac
Or 9= x*3x/2
Or 9= 3x^2/2
Or 3x^2= 9
Or x^2= 3
So x= √3
So ac= 3√3
We know that,
Ab^2= ac^2+ bc^2
= (3√3)^2+ √3^2
= 9×3+3
=30
Ab=√30

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Re: Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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New post 09 Oct 2018, 02:18
rumel1991 wrote:
Let bc = x, so ac=3x
We know that,
Area of traigle = 1/2*bc*ac
Or 9= x*3x/2
Or 9= 3x^2/2
Or 3x^2= 18
Or x^2= 6
So x= √6
So ac= 3√6
We know that,
Ab^2= ac^2+ bc^2
= (3√6)^2+ √6^2
= 9×6+6
=60
Ab=√60
=√4×15
2√15
Ans:2√15

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Re: Triangle ABC has an area of 9. If AC is three times as long as CB, wha   [#permalink] 09 Oct 2018, 02:18
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