document.write( "Question 260707: What is the best approximation of the perimeter of a right isosceles triangle if its hypotenuse is 12 units long? what is its area? \n" ); document.write( "
Algebra.Com's Answer #192078 by drk(1908)\"\" \"About 
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The issue here is that we don't know the other two sides. By the triangle inequality theorem, we know that they are greater than 12.
\n" ); document.write( "we also know a^2 + b^2 = c^2, where c = 12
\n" ); document.write( "We have several options
\n" ); document.write( "a = 1, b = sqrt(143), c = 12, P =
\n" ); document.write( "a = 2, b = sqrt(140), c = 12, P =
\n" ); document.write( "a = 3. b = sqrt(135), c = 12, P =
\n" ); document.write( "a = 4, b = sqrt(128), c = 12, P =
\n" ); document.write( "a = 5, b = sqrt(119), c = 12, P =
\n" ); document.write( "a = 6, b = sqrt(108), c = 12, P =
\n" ); document.write( "a = 7, b = sqrt(95), c = 12, P =
\n" ); document.write( "a = 8, b = sqrt(80), c = 12, P =
\n" ); document.write( "a = 9, b = sqrt(63), c = 12, P =
\n" ); document.write( "a = 10, b = sqrt(44), c = 12, P =
\n" ); document.write( "a = 11, b = sqrt(23), c = 12, P =
\n" ); document.write( "----
\n" ); document.write( "The average of all perimeters is ~ 26.64377
\n" ); document.write( "The missing sides a and b could be ~ 7.821
\n" ); document.write( "--
\n" ); document.write( "we use herons formula to estimate the area
\n" ); document.write( "we need S = (7.821 + 7.821 + 12)/2 = 13.821
\n" ); document.write( "A ~ sqrt(13.821(13.821-7.821)(13.821-7.821)(13.821-12))
\n" ); document.write( "A ~ 30.1089 \n" ); document.write( "
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