document.write( "Question 17499: I have an equilateral triangle with an area of 30 square centimeters. I need to find the base and height of the triangle. \n" ); document.write( "
Algebra.Com's Answer #8570 by xcentaur(357)\"\" \"About 
You can put this solution on YOUR website!
For an equilateral triangle,
\n" ); document.write( "Area is given by
\n" ); document.write( "\"+A=+%28s%5E2%29sqrt%283%29%2F4+\"
\n" ); document.write( "where s is the length of the side
\n" ); document.write( "


\n" ); document.write( "\"+30+=+s%5E2%2Asqrt%283%29%2F4+\"
\n" ); document.write( "\"+30%2A4%2Fsqrt%283%29+=+s%5E2+\"
\n" ); document.write( "\"+3%2A40%2Fsqrt%283%29+=+s%5E2+\"
\n" ); document.write( "\"+sqrt%283%29%2A40+=+s%5E2+\"
\n" ); document.write( "\"+s=+sqrt%2840%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+s=+sqrt%28sqrt%2840%2A40%2A3%29%29+\"
\n" ); document.write( "\"+s=+sqrt%28sqrt%284800%29%29+\"
\n" ); document.write( "Clear till here? Good.
\n" ); document.write( "Now we have to take factors twice.
\n" ); document.write( "So we get
\n" ); document.write( "\"+sqrt%284800%29=40%2Asqrt%283%29+\" ........[first time]
\n" ); document.write( "\"+sqrt%2840%2Asqrt%283%29%29=2%2Asqrt%285%29%2Asqrt%282%29%2Asqrt%283%29\"......[second time]
\n" ); document.write( "\"+sqrt%2840%2Asqrt%283%29%29=2%2Asqrt%2810%2Asqrt%283%29%29\"......[simplified]
\n" ); document.write( "Therefore we get our value of 's' as \"2%2Asqrt%2810%2Asqrt%283%29%29\"
\n" ); document.write( "


\n" ); document.write( "\"+A=+%28s%5E2%29sqrt%283%29%2F4+=+%281%2F2%29bh+\"
\n" ); document.write( "Now base and side are equal,therefore
\n" ); document.write( "\"+%28s%5E2%29sqrt%283%29%2F4+=+%281%2F2%29bh+\"
\n" ); document.write( "\"+%28s%5E2%29sqrt%283%29%2F4+=+%281%2F2%29sh+\"
\n" ); document.write( "\"+s%2Asqrt%283%29%2F4+=+%281%2F2%29h+\"
\n" ); document.write( "\"+s%2Asqrt%283%29%2F2+=+h+\"
\n" ); document.write( "\"+h+=+%28sqrt%283%29%2F2%29%2A2%2Asqrt%2810%2Asqrt%283%29%29\"
\n" ); document.write( "\"+h+=+sqrt%283%29%2Asqrt%2810%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+h=+sqrt%283%2A10%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+h=+sqrt%2830%2Asqrt%283%29%29+\"
\n" ); document.write( "


\n" ); document.write( "So we have our values as
\n" ); document.write( "\"+s+=+2%2Asqrt%2810%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+h+=+sqrt%2830%2Asqrt%283%29%29+\"
\n" ); document.write( "


\n" ); document.write( "We can verify this using the [A=1/2bh] formula,
\n" ); document.write( "Area=1/2*s*h
\n" ); document.write( "\"+%281%2F2%29%2A2%2Asqrt%2810%2Asqrt%283%29%29%2Asqrt%2830%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+sqrt%2810%2Asqrt%283%29%2A30%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+sqrt%28300%2Asqrt%283%29%2Asqrt%283%29%29+\"
\n" ); document.write( "\"+sqrt%28300%2A3%29+\"
\n" ); document.write( "\"+sqrt%28900%29+\"
\n" ); document.write( "\"+30+\"
\n" ); document.write( "


\n" ); document.write( "And thus we know that our values for s and h are correct.
\n" ); document.write( "Hope this helps,
\n" ); document.write( "Prabhat \n" ); document.write( "

\n" );