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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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Joined: 02 Sep 2009
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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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09 Oct 2018, 00:57
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Difficulty:

15% (low)

Question Stats:

92% (01:35) correct 8% (00:00) wrong based on 13 sessions

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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) $$15$$

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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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09 Oct 2018, 01:05
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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09 Oct 2018, 01:06
Bunuel wrote:

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=$$\sqrt{60}$$
$$AB = 2\sqrt{15}$$

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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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09 Oct 2018, 01:13

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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09 Oct 2018, 01:14
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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Joined: 03 Oct 2018
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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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09 Oct 2018, 01:18
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, 01:18
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