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Triangle ABC has an area of 9. If AC is three times as long
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26 Sep 2018, 15:45
26 Sep 2018, 15:45
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82% (01:45) correct
17% (01:22) wrong based on 52 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
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06 Dec 2018, 15:40
06 Dec 2018, 15:40
1
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
Re: Triangle ABC has an area of 9. If AC is three times as long
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03 Jun 2022, 03:20
03 Jun 2022, 03:20
thank you
