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Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, one side = x and the other side = x+7. I'm not sure what to do next though.
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\n" ); document.write( "From here, you apply Pythagorean theorem:
\n" ); document.write( "a^2 + b^2 = c^2
\n" ); document.write( "where
\n" ); document.write( "c is length of hypotenuse
\n" ); document.write( "a and b are the lengths of the two sides
\n" ); document.write( ".
\n" ); document.write( "x^2 + (x+7)^2 = (x+9)^2
\n" ); document.write( "x^2 + (x+7)(x+7) = (x+9)(x+9)
\n" ); document.write( "x^2 + (x^2+14x+49) = (x^2+18x+81)
\n" ); document.write( "2x^2+14x+49 = x^2+18x+81
\n" ); document.write( "x^2 - 4x - 32 = 0
\n" ); document.write( "Factoring:
\n" ); document.write( "(x-8)(x+4) = 0
\n" ); document.write( "x = {-4, 8}
\n" ); document.write( "We can throw out the negative solution leaving:
\n" ); document.write( "x = 8 cm (short leg)
\n" ); document.write( ".
\n" ); document.write( "long leg:
\n" ); document.write( "x+7 = 8+7 = 15 cm
\n" ); document.write( ".
\n" ); document.write( "hypotenuse:
\n" ); document.write( "x+9 = 8+9 = 17 cm\r
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