document.write( "Question 1148735: At a certain time of day a tree that is X meters tall cast a shadow that is X -3 m long if the distance from the top of the tree to the end of the shadow is X +1 m what is the height X of the tree \n" ); document.write( "
Algebra.Com's Answer #770080 by ankor@dixie-net.com(22740)\"\" \"About 
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At a certain time of day a tree that is X meters tall cast a shadow that is X -3 m long
\n" ); document.write( " if the distance from the top of the tree to the end of the shadow is X +1 m, what is the height X of the tree
\n" ); document.write( ":
\n" ); document.write( "This forms a right triangle: a^2 + b^2 = c^2; where
\n" ); document.write( "a = x
\n" ); document.write( "b = (x-3)
\n" ); document.write( "c = (x+1)
\n" ); document.write( "Using Pythagoras we have
\n" ); document.write( "x^2 + (x-3)^2 = (x+1)^2
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + x^2 - 6x + 9 = x^2 + 2x + 1
\n" ); document.write( "Combine like terms on the left
\n" ); document.write( "x^2 + x^2 - x^2 - 6x - 2x + 9 - 1 = 0
\n" ); document.write( "x^2 - 8x + 8 = 0
\n" ); document.write( "Use the quadratic formula a=1; b=-8; c=8
\n" ); document.write( "the two solutions
\n" ); document.write( "x = 1.17
\n" ); document.write( "and
\n" ); document.write( "x = 6.83, this is the only solution that makes sense (x-3)
\n" ); document.write( "therefore the tree is 6.83 m high
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check: find the hypotenuse using 6.83 and 3.83
\n" ); document.write( "h = \"sqrt%286.83%5E2+%2B+3.83%5E2%29\"
\n" ); document.write( "h = 7.83 which is x+1
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