document.write( "Question 242582: An isoscles right triangle has a perimeter of 25 inches, what is the length of the hypotenuse to the nearest ten thousandth?\r
\n" ); document.write( "\n" ); document.write( "Please help, thank you very much! \n" ); document.write( "
Algebra.Com's Answer #177597 by unlockmath(1688)\"\" \"About 
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Hello,
\n" ); document.write( "This involves a few steps. First, we know that the two sides of the triangle are the same, so let's represent them with x. We'll let y represent the hypotenuse. We can set up 2 equations which are:
\n" ); document.write( "x+x+y=25 or rewritten as 2x+y=25 or y=25-2x (And the other equation can be):
\n" ); document.write( "x^2+x^2=y^2 or rewritten as 2x^2=y^2
\n" ); document.write( "With substitution we can do the following:
\n" ); document.write( "2x^2= (25-2x)^2 This expands out to:
\n" ); document.write( "2x^2=4x^2-100x+625 Subtract 2x^2 from both sides gives us:
\n" ); document.write( "0=2x^2-100x+625 Using the Quadratic formula
\n" ); document.write( "{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }} plug in the numbers:
\n" ); document.write( "{{x = (100 +- sqrt( 10000-5000 ))/(2*2) }} turns out to be:
\n" ); document.write( "x=42.6776 or
\n" ); document.write( "x=7.3223 (this makes sense so plug it in the original equation)
\n" ); document.write( "2(7.3223)+y=25
\n" ); document.write( "14.6447+y=25
\n" ); document.write( "y=10.3553
\n" ); document.write( "This can be checked by adding the sides which are
\n" ); document.write( "7.3223 Inches
\n" ); document.write( "7.3223 Inches
\n" ); document.write( "10.3553 inches which totals approx 25 inches.
\n" ); document.write( "There you go. I hope this is clear for you.
\n" ); document.write( "RJ Toftness
\n" ); document.write( "www.math-unlock.com
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