document.write( "Question 495945: The diagonal of a rectangle is 10cm and the area of the rectangle is 22 cm^2. Find the perimeter of the rectangle \n" ); document.write( "
Algebra.Com's Answer #336279 by cleomenius(959)\"\" \"About 
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We will use two formulas.
\n" ); document.write( "First the formula for the area of a triangle, to obtain a value for y.
\n" ); document.write( "1/2*xy = 11 so y = 22/x
\n" ); document.write( "Now we substitute into y for the Pythagorean theory.
\n" ); document.write( "x^2 + y^2 = 10^2
\n" ); document.write( "x^2 + (22/x)^2 = 100
\n" ); document.write( "This equates to
\n" ); document.write( "x^4 -100x^2 + 484= 0
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\n" ); document.write( "Now we the Quadratic formula:
\n" ); document.write( "a = 1
\n" ); document.write( "b= -100
\n" ); document.write( "c = 484
\n" ); document.write( "We obtain:
\n" ); document.write( "x^2 = 94.9, 4.93
\n" ); document.write( "x = 9.74, 2.25
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\n" ); document.write( "To check:
\n" ); document.write( "9.74 * 2.25 = 21.915, approx 22.
\n" ); document.write( "Also
\n" ); document.write( "(9.74)^2 = 94.87
\n" ); document.write( "(2.25)^2 = 5.07
\n" ); document.write( "94.87 + 5.07 = 99.94 = diameter^2 = approx 10.
\n" ); document.write( "This does check.
\n" ); document.write( "Cleomenius. \n" ); document.write( "
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