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When rescuing a woman from a burning building, fireman found that the height of
\n" ); document.write( " the window she was leaning out of was 1m less than the length of the ladder.
\n" ); document.write( "The distance from the foot of the ladder to the building was 8m less than the length of the ladder.
\n" ); document.write( " Find the length of the ladder.
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\n" ); document.write( "Let x = length of the ladder
\n" ); document.write( "then
\n" ); document.write( "(x-1) = height of the window
\n" ); document.write( "and
\n" ); document.write( "(x-8) = distance from building to base of the ladder
\n" ); document.write( ":
\n" ); document.write( "This forms a right triangle we can solve, a^2 + b^2 = c^2
\n" ); document.write( "In this problem
\n" ); document.write( "x = c, the hypotenuse
\n" ); document.write( "(x-1) = a
\n" ); document.write( "(x-8) = b
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\n" ); document.write( "so we have
\n" ); document.write( "(x-1)^2 + (x-8)^2 = x^2
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\n" ); document.write( "FOIL
\n" ); document.write( "(x^2 - 2x + 1) + (x^2 - 16x + 64) = x^2
\n" ); document.write( ":
\n" ); document.write( "Combine like terms
\n" ); document.write( "x^2 + x^2 - x^2 - 2x - 16x + 1 + 64 = 0
\n" ); document.write( ":
\n" ); document.write( "a quadratic equation
\n" ); document.write( "x^2 - 18x + 65 = 0
\n" ); document.write( ":
\n" ); document.write( "Factors to
\n" ); document.write( "(x-5)(x-13) = 0
\n" ); document.write( ":
\n" ); document.write( "Two solutions but only one is reasonable
\n" ); document.write( "x = 13 meters is the length of the ladder
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\n" ); document.write( ":
\n" ); document.write( "See if the works out
\n" ); document.write( "12^2 + 5^2 = 13^2
\n" ); document.write( "144 + 25 = 169, confirms our solution of x=13 \n" ); document.write( "