document.write( "Question 256013: If a 30° - 60° - 90° triangle has a perimeter of 12 units and its area is in the form of (a√b - c), then determine the numerical value of (a + b + c). \n" ); document.write( "

Algebra.Com's Answer #188197 by drk(1908) $\"\"$ $\"About$

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Let side opposite 90 = x
\n" ); document.write( "Let side opposite 30 = (1/2)x
\n" ); document.write( "Let side opposite 60 = (sqrt(3)/2)x
\n" ); document.write( "Perimeter = 12, so
\n" ); document.write( "(i) $\"x+%2B+%281%2F2%29x+%2B+%28sqrt%283%29%2F2%29x+=+12\"$
\n" ); document.write( "solving for x, we get
\n" ); document.write( "(ii) $\"%283%2F2%29x+%2B+%28sqrt%283%29%2F2%29x+=+12\"$
\n" ); document.write( "multiply by 2 to get
\n" ); document.write( "(iii) $\"3x+%2B+x%2Asqrt%283%29+=+24\"$
\n" ); document.write( "factor out an x to get
\n" ); document.write( "(iv) $\"x%283%2Bsqrt%283%29%29+=+24\"$
\n" ); document.write( "dividing, we get
\n" ); document.write( "(v) $\"x+=+24%2F%283%2Bsqrt%283%29%29\"$
\n" ); document.write( "So,
\n" ); document.write( "side opposite 90 = 24/(3+sqrt(3))
\n" ); document.write( "side opposite 30 = 12/(3+sqrt(3))
\n" ); document.write( "side opposite 60 = 12sqrt(3)/(3+sqrt(3))
\n" ); document.write( "using these 3 lengths, our perimeter =12.
\n" ); document.write( "we want a + b + c values. I think we have them. The area formula is a bit confusing. \n" ); document.write( "

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