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 CBLet x = length of CB

So, 3x = length of AC

Triangle ABC has an area of 9Area = (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

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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