document.write( "Question 684555: the diagonal of a rectangle is 2 centimeters longer than its length and 9 centimeters greater than its width. find the dimensions of the rectangle. \n" ); document.write( "
Algebra.Com's Answer #424352 by Jolliano(16)\"\" \"About 
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Let d be length of diagonal,h be height and w be width.
\n" ); document.write( "The length,width and diagonal form a right angled triangle with the diagonal as the hypotenuse.
\n" ); document.write( "From the question,
\n" ); document.write( "d = h + 2 .........(1) and
\n" ); document.write( "d = w + 9 ........(2).
\n" ); document.write( "Equating both,
\n" ); document.write( "h + 2 = w + 9
\n" ); document.write( "h = w + 9 - 2
\n" ); document.write( "h = w +7..............(3)
\n" ); document.write( "Using Pythagoras theorem,
\n" ); document.write( "h^2 + w^2 = d^2
\n" ); document.write( "Sub h with (3) and d with (2)
\n" ); document.write( "(w + 7)^2 + w^2 = (w + 9)^2
\n" ); document.write( "w^2 + 14w + 49 + w^2 = w^2 +18w + 81
\n" ); document.write( "Collecting like terms,
\n" ); document.write( "w^2 - 4w - 32= 0
\n" ); document.write( "Factorizing,
\n" ); document.write( "(w + 4)(w - 8) = 0
\n" ); document.write( "w = -4 or 8.
\n" ); document.write( "The Width cannot be negative so
\n" ); document.write( "Width = 8cm
\n" ); document.write( "From (3)
\n" ); document.write( "h = w + 7 = 8 + 7 = 15cm.
\n" ); document.write( "From (2)
\n" ); document.write( "d = w + 9 = 8 + 9 = 17cm. \n" ); document.write( "
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