document.write( "Question 760230: A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side. The third side is 1 cm less than twice the shortest side.
\n" ); document.write( "Find the length (in cm) of the hypotenuse? \n" ); document.write( "

Algebra.Com's Answer #462491 by ramkikk66(644) $\"\"$ $\"About$

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Let the shortest side be x
\n" ); document.write( "Then the hypotenuse is $\"2%2Ax+%2B+1\"$
\n" ); document.write( "3rd side is $\"2%2Ax+-+1\"$
\n" ); document.write( "Pythagoras theorem:
\n" ); document.write( "Square of hypotenuse = sum of squares of other 2 sides.\r
\n" ); document.write( "\n" ); document.write( "So, $\"%282x+%2B+1%29%5E2+=+x%5E2+%2B+%282x+-+1%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "Expanding:\r
\n" ); document.write( "\n" ); document.write( " $\"4x%5E2+%2B+4x+%2B+1+=+x%5E2+%2B+%284x%5E2+-+4x+%2B+1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " [Using the formulae for $\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"$ ]\r
\n" ); document.write( "\n" ); document.write( "Simplifying:
\n" ); document.write( " $\"4x+=+x%5E2+-+4x\"$ , or \r
\n" ); document.write( "\n" ); document.write( "4 = x - 4.
\n" ); document.write( "i.e. x = 8.
\n" ); document.write( "So, the 3 sides are 8, 15 and 17 (hypotenuse)\r
\n" ); document.write( "\n" ); document.write( "To check, apply the pythagoras theorem.
\n" ); document.write( "8^2 = 64 (square of 1 side)
\n" ); document.write( "15^2 = 225 (square of the 2nd side)
\n" ); document.write( "17^2 = 289 (square of hypotenuse)
\n" ); document.write( "64 + 225 = 289, so the answer is correct. Length of hypotenuse = 17 cm.
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