document.write( "Question 1105588: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27√3 cm2. What is the side lenght AB, in cm?
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Algebra.Com's Answer #720490 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The altitude of an equilateral triangle is also a median. If AE is a median of triangle ABD, then the base of triangle AEC is 3/4 the side length of the equilateral triangle.

\n" ); document.write( "If the area of triangle AEC is $\"27%2Asqrt%283%29\"$ , then the area of the equilateral triangle is 4/3 of that, or $\"36%2Asqrt%283%29\"$ .

\n" ); document.write( "The area of an equilateral triangle is $\"%28s%5E2%2Asqrt%283%29%29%2F4\"$ , so
\n" ); document.write( " $\"%28s%5E2%2Asqrt%283%29%29%2F4+=+36%2Asqrt%283%29\"$
\n" ); document.write( " $\"s%5E2+=+144\"$
\n" ); document.write( " $\"s+=+12\"$

\n" ); document.write( "The side length of the equilateral triangle is 12 cm. \n" ); document.write( "

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