document.write( "Question 1166466: PQRS is a rectangle in which PQ=10 and PS=6. T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST. Find RT
\n" ); document.write( "How do we get ST=6?
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Algebra.Com's Answer #791010 by ankor@dixie-net.com(22740)\"\" \"About 
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PQRS is a rectangle in which PQ=10 and PS=6.
\n" ); document.write( " T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST.
\n" ); document.write( " Find RT
\n" ); document.write( ":
\n" ); document.write( "Draw this out. We know that St = 10 also from the information given
\n" ); document.write( "label the line segment TQ as x
\n" ); document.write( "We can find x using the right triangle PST, where
\n" ); document.write( "side PS given as 6 and the other side (10-x), ST = 10 the hypotenuse
\n" ); document.write( "solve for x using pythag
\n" ); document.write( "6^2 + (10-x)^2 = 10^2
\n" ); document.write( "36 + 100 - 20x + x^2 = 100
\n" ); document.write( "Subtract 100 from both sides and arrange as a simple quadratic equation
\n" ); document.write( "x^2 - 20x + 36 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-2)(x-18) = 0
\n" ); document.write( "The reasonable solution
\n" ); document.write( "x = 2
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\n" ); document.write( "Use the right triangle TQR, where one leg = 2, one leg = 6
\n" ); document.write( "Find RT which is the hypotenuse
\n" ); document.write( "RT = \"sqrt%282%5E2+%2B+6%5E2%29\"
\n" ); document.write( "RT = 6.32 \n" ); document.write( "
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