document.write( "Question 122278: I keep coming up with a solution that is different from the answer key. Here is the problem: Find the area of an isosceles triangle where the base is 3 and the sides are the square root of 11.
\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #89793 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Triangle is ABC.
\n" ); document.write( "AB side is $\"sqrt%2811%29\"$ .
\n" ); document.write( "AC side is $\"sqrt%2811%29\"$ .
\n" ); document.write( "BC side is $\"3\"$ .
\n" ); document.write( "Split BC in half at point Z to form two equal line segments BZ=ZC=3/2.
\n" ); document.write( "You can now form two right triangles, ABZ and AZC.
\n" ); document.write( "Call the length of AZ side, H.
\n" ); document.write( "Using the Pythagorean theorem, you can find the height, H, because,
\n" ); document.write( " $\"H%5E2%2B%283%2F2%29%5E2=%28sqrt%2811%29%29%5E2\"$
\n" ); document.write( " $\"H%5E2%2B%289%2F4%29=11\"$
\n" ); document.write( " $\"H%5E2=11-%289%2F4%29\"$
\n" ); document.write( " $\"H%5E2=44%2F4-9%2F4\"$
\n" ); document.write( " $\"H%5E2=36%2F4\"$
\n" ); document.write( " $\"H%5E2=9\"$
\n" ); document.write( " $\"H=3\"$
\n" ); document.write( "For the area of the original isoceles triangle,
\n" ); document.write( " $\"A=%281%2F2%29bH\"$
\n" ); document.write( " $\"A=%281%2F2%29%283%2F2%29%283%29\"$
\n" ); document.write( " $\"A=9%2F4\"$
\n" ); document.write( "A is 2.25 square units.
\n" ); document.write( "Does that answer match the answer key? \n" ); document.write( "

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