document.write( "Question 120959: A square and an equilateral triangle have equal perimeters. The area of the triangle is 9 root 3 square inches. Express, in inches, the length of a diagonal of the square. \n" ); document.write( "
Algebra.Com's Answer #88757 by edjones(8007)\"\" \"About 
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Let a=altitude, b=base A=area
\n" ); document.write( "A=.5ab
\n" ); document.write( "Construct an altitude into the equilateral triangle. Let c=hypotenuse. b=c/2.
\n" ); document.write( "If b=1 and c=2 then a^2+1^2=2^2
\n" ); document.write( "a^2=3
\n" ); document.write( "a=sqrt(3)
\n" ); document.write( "The triangle must be similar to a triangle with a base of 2 and an altitude of sqrt(3)
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\n" ); document.write( ".5ab=A
\n" ); document.write( ".5*x*sqrt(3)*2x=9sqrt(3) The x is in there to determine how many times larger this triangle is than the 1-2-sqrt(3) similar right triangle.
\n" ); document.write( "x^2=9
\n" ); document.write( "x=3
\n" ); document.write( "The sides of the triangle are 2x or 6\"
\n" ); document.write( "6*3=18 Perimeter of triangle and square.
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\n" ); document.write( "side of the square=18/4=4.5\"
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\n" ); document.write( "a^2+b^2=c^2 (c is the diagonal of the square.)
\n" ); document.write( "4.5^2*2=c^2
\n" ); document.write( "c^2=40.5
\n" ); document.write( "c=6.36396\"
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