document.write( "Question 1168590: The hypotenuse of a right angle triangle is 15 cm. One of the legs is 2 and half times the length of the other
\n" ); document.write( "leg. What is the length of the longer leg? Please use fractions when solving, not decimals, until the unknown
\n" ); document.write( "variable is collected to one side of the equation. Your final answer will be in decimal form.\r
\n" ); document.write( "\n" ); document.write( "Please HELP ME I REALLY NEED THIS THANK YOU! \n" ); document.write( "
Algebra.Com's Answer #793168 by Theo(13342)\"\" \"About 
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the hypotenuse is 15.
\n" ); document.write( "one of the legs is 2 and 1/2 * the length of the other leg.
\n" ); document.write( "let one of the legs be equal to x.
\n" ); document.write( "the other leg is then 2.5 * x
\n" ); document.write( "since hypotenuse squared = sum of the square of each leg, your equation becomes:
\n" ); document.write( "x^2 + (2.5 * x)^2 = 15^2
\n" ); document.write( "simplify to get x^2 + 6.25x^2 = 225
\n" ); document.write( "simplify further to get 7.25x^2 = 225
\n" ); document.write( "solve for x to get x = sqrt(225/7.25) = 5.570860145
\n" ); document.write( "x = 5.270860145
\n" ); document.write( "2.5 * x = 13.92715036
\n" ); document.write( "with these values, x^2 + (2.5*x)^2 = 225
\n" ); document.write( "sqrt(225) = 15, confirming the solution is correct.
\n" ); document.write( "let x = one of the legs.
\n" ); document.write( "the other leg is 2.5 * as large which makes the other leg equal to \r
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\n" ); document.write( "\n" ); document.write( "that was not, however, done using fractions.
\n" ); document.write( "let's try again using fractions.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "one leg is equal to x.
\n" ); document.write( "the other leg is equal to 2.5 * x = (2 + 1/2) * x = 5/2 * x
\n" ); document.write( "the sum of the squares of each leg is equal to the hypotenuse squared.
\n" ); document.write( "you get x^2 + (5/2 * x)^2 = 15^2
\n" ); document.write( "simplify to get x^2 + 25/4 * x^2 = 225
\n" ); document.write( "x^2 = 1 * x^2 and 1 = 4/4, so x^2 = 4/4 * x^2 and the equation becomes:
\n" ); document.write( "4/4 * x^2 + 25/4 * x^2 = 225
\n" ); document.write( "factor out the x^2 to get:
\n" ); document.write( "(4/4 + 25/4) * x^2 = 225
\n" ); document.write( "simplify to get:
\n" ); document.write( "29/4 * x^2 = 225
\n" ); document.write( "multiply both sides of this equation by 4/29 to get:
\n" ); document.write( "4/29 * 29/4 * x^2 = 4/29 * 225
\n" ); document.write( "simplify to get:
\n" ); document.write( "x^2 = 4/29 * 225
\n" ); document.write( "simplify to get x^2 = 900/29
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = sqrt(900/29) = sqrt(900)/sqrt(29)
\n" ); document.write( "sqrt(900) = 30
\n" ); document.write( "sqrt(29) does not appear to be a rational number and so must be left as sqrt(29).
\n" ); document.write( "your answer will be that x = 30/sqrt(29).
\n" ); document.write( "2.5 * x will be equal to 5/2 * 30/sqrt(29) = (5*30)/(2*sqrt(29)) = 75/sqrt(29).\r
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\n" ); document.write( "\n" ); document.write( "30/sqrt(29) = 5.570860145, same as i got using decimals.
\n" ); document.write( "75/sqrt(29) = 13.92715036, same as i got using decimals.\r
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\n" ); document.write( "\n" ); document.write( "the answer appears to be the same whether i used decimals or fractions, as it should.\r
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