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a lot is shaped like a right triangle. the hypotenuse is three meters longer than the longer leg. the longer leg is six meters longer than twice the length of the shorter leg. find the lengths of all three sides on the triangular lot.
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\n" ); document.write( "Let x = the length of the shorter leg (side a)
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\n" ); document.write( "Write an expression for each statement:
\n" ); document.write( "\"the longer leg is six meters longer than twice the length of the shorter leg\" side (b)
\n" ); document.write( "longer leg = (2x + 6)
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\n" ); document.write( "\"The hypotenuse is three meters longer than the longer leg\" (side c)
\n" ); document.write( "hypotenuse = (2x + 6) + 3
\n" ); document.write( "hypotenuse = (2x + 9)
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\n" ); document.write( "Remember that; a^2 + b^2 = c^2, in a right triangle
\n" ); document.write( "x^2 + (2x+6)^2 = (2x+9)^2
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\n" ); document.write( "x^2 + 4x^2 + 24x + 36 = 4x^2 + 36x + 81; FOILed
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\n" ); document.write( "x^2 + 4x^2 - 4x^2 + 24x - 36x + 36 - 81 = 0; arrange all terms on the left
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\n" ); document.write( "x^2 - 12x - 45 = 0; a quadratic equation
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\n" ); document.write( "Factors to:
\n" ); document.write( "(x-15)(x+3) = 0
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\n" ); document.write( "x = -3
\n" ); document.write( "and
\n" ); document.write( "x = +15 is the length of the shorter leg
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\n" ); document.write( "2(15) + 6 = 36 is the length of the longer leg
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\n" ); document.write( "2(15) + 9 = 39 is the hypotenuse
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\n" ); document.write( "Check solution using a^2 + b^2 = c^2:
\n" ); document.write( " 15^2 + 36^2 = 1521 which is 39^2 \n" ); document.write( "