document.write( "Question 388451: The length of the diagonal of a square is the perimeter of a right triangle,
\n" ); document.write( "and the lengths of the shorter two sides of the triangle are 3 and 4, find
\n" ); document.write( "the area of the square in square units. \n" ); document.write( "
Algebra.Com's Answer #274776 by nerdybill(7384)\"\" \"About 
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The length of the diagonal of a square is the perimeter of a right triangle,
\n" ); document.write( "and the lengths of the shorter two sides of the triangle are 3 and 4, find
\n" ); document.write( "the area of the square in square units.
\n" ); document.write( ".
\n" ); document.write( "First, determine perimeter of right triangle.
\n" ); document.write( "applying Pythagorean theorem we get:
\n" ); document.write( "Let h = hypotenuse
\n" ); document.write( "then
\n" ); document.write( "3^2 + 4^2 = h^2
\n" ); document.write( "9 + 16 = h^2
\n" ); document.write( "25 = h^2
\n" ); document.write( "5 = h
\n" ); document.write( ".
\n" ); document.write( "perimeter = 5 + 3 + 4 = 12
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\n" ); document.write( "Let s = length of one side of square
\n" ); document.write( "then
\n" ); document.write( "s^2 + s^2 = 12^2
\n" ); document.write( "2s^2 = 144
\n" ); document.write( "s^2 = 72
\n" ); document.write( "s = sqrt(72)
\n" ); document.write( "s = sqrt(6*6*2)
\n" ); document.write( "s = 6sqrt(2) (this is the exact answer)
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\n" ); document.write( "Decimal approximation:
\n" ); document.write( "s = 8.49\r
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