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# Triangle ABC has an area of 9. If AC is three times as long

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Triangle ABC has an area of 9. If AC is three times as long [#permalink]  26 Sep 2018, 15:45
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Question Stats:

88% (01:57) correct 11% (00:00) wrong based on 17 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) $$15$$
[Reveal] Spoiler: OA

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Re: Triangle ABC has an area of 9. If AC is three times as long [#permalink]  06 Dec 2018, 15:40
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sandy 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) $$15$$

AC is three times as long as CB
Let x = length of CB
So, 3x = length of AC

Triangle ABC has an area of 9
Area = (base)(height)/2
So: 9 = (x)(3x)/2
Simplify: 9 = 3x²/2
Multiply both sides by 2 to get: 18 = 3x²
Divide both sides by 3 to get: 6 = x²
Solve: x = √6

So, side CB has length √6, which means side AC has length 3√6

What is the length of AB?
Let y = the length of AB

Since we have a right triangle, we can apply the Pythagorean Theorem.
We get: (√6)² + (3√6)² = y²
Simplify: 6 + 54 = y²
Simplify: 60 = y²
Solve: y = √60
So, the length of AB = √60 . . . not among the answer choices. Looks like we need to simplify √60

√60 = √[(4)(15)] = (√4)(√15) = 2√15

Answer: C

Cheers,
Brent
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Re: Triangle ABC has an area of 9. If AC is three times as long   [#permalink] 06 Dec 2018, 15:40
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# Triangle ABC has an area of 9. If AC is three times as long

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