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HOW AE =SQUAREROOT 3+AC?
CAN YOU PLZ EXPLAIN ME THIS?
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CDE is right angle triangle.
ED = 1
CD= 2
Then CE = sqrt(3) . This is followed by properties of right angle triangle.
(1, sqrt3, 2) indicates angle 30°-60°-90°

Hope it clarifies your doubt.
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HOW AE =SQUAREROOT 3+AC?
CAN YOU PLZ EXPLAIN ME THIS?
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Bunuel

Note: Figure not drawn to scale.

In the figure above, ED = 1, CD = 2, and \(AE = 6\sqrt{3}\). What is the perimeter of ΔABC ?

A. \(3\sqrt{3}\)
B. \(10+5\sqrt{3}\)
C. \(10\sqrt{3}\)
D. \(15+5\sqrt{3}\)
E. \(25\sqrt{3}\)

Attachment:
2015-12-27_2122.png

Let's look at CDE first.
\(1^2+CE^2 = 2^2\)

\(1+CE^2 = 4\)

\(CE^2 = 3\)

\(CE = \sqrt{3}\)

Perimeter of CDE = \(1+2+\sqrt{3}\) = \(3+\sqrt{3}\)

AE = \(6\sqrt{3}\) and CE = \(\sqrt{3}\), so AC = \(5\sqrt{3}\).

ABC and CDE are similar triangles. The longer leg of ABC is 5x the longer leg of CDE, so the perimeter is 5x.

\(5(3+\sqrt{3}) = 15+5\sqrt{3}\)

Answer choice D.
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