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Math Expert V
Joined: 02 Sep 2009
Posts: 58458
Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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Difficulty:   15% (low)

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

HideShow timer Statistics 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 [ 10.58 KiB | Viewed 479 times ]

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

The best answer is C.
Senior PS Moderator V
Joined: 26 Feb 2016
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Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

Show Tags 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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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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Intern  Joined: 03 Oct 2018
Posts: 4
Re: Triangle ABC has an area of 9. If AC is three times as long as CB, wha  [#permalink]

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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

Posted from my mobile device 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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