document.write( "Question 1040474: PQRS is a parallelogram with PQ=2x cm, QR=x cm and angle PQR=110°. If the parallelogram have an area of 93.5304 cm², find the value of x. \n" ); document.write( "
Algebra.Com's Answer #655289 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the area of a parallelogram is equal to base * height.
\n" ); document.write( "pq and rs are lengths of the parallelogram, each of which has a length of 2x.
\n" ); document.write( "qr and sp are widths of the parallelogram, each of which has a length of x.
\n" ); document.write( "for purposes of calculating the area of the parallelogram, rs is the base.
\n" ); document.write( "the opposite angles of a parallelogram are equal and the adjacent angles of a parallelogram are supplementary.
\n" ); document.write( "this means:
\n" ); document.write( "angle pqr = 110
\n" ); document.write( "angle qrs = 70
\n" ); document.write( "andle rsp = 110
\n" ); document.write( "angle spq= 70
\n" ); document.write( "drop a perpendicular from point q to intersect with line sr at point w.
\n" ); document.write( "qw becomes the height of the parallelogram.
\n" ); document.write( "this forms right triangle qrw.
\n" ); document.write( "qr is the hypotenuse of this triangle whose length is equal to x.
\n" ); document.write( "angle qrw is equal to 70 degrees.
\n" ); document.write( "qw is the side opposite angle qrw whose length is equal to h.
\n" ); document.write( "to find h in terms of x, use trig function of sin(70) = opp/hyp = h/x
\n" ); document.write( "solve for h to get h = x*sin(70).
\n" ); document.write( "the area of the parallelogram is equal to base * height.
\n" ); document.write( "base has a length of 2x (given).
\n" ); document.write( "the area is therefore equal to 2x * h
\n" ); document.write( "replace h with x*sin(70) to get area = 2*x*x*sin(70).
\n" ); document.write( "simplify to get area = 2*x^2*sin(70).
\n" ); document.write( "divide both sides of the equation by 2*sin(70) to get area/(2*sin(70)) = x^2.
\n" ); document.write( "area = 93.5304 (given).
\n" ); document.write( "formula becomes 93.5304/(2*sin(70)) = x^2.
\n" ); document.write( "solve for x^2 to get x^2 = 93.5304/(2*sin(70)).
\n" ); document.write( "take square root of both sides of the equation to get x = sqrt(93.5304/(2*sin(70))).
\n" ); document.write( "this makes x = 7.05453658
\n" ); document.write( "the diagram of your parallelogram is shown below:
\n" ); document.write( "point w is not marked (an oversight).
\n" ); document.write( "it is the intersection of the line from point q to the line sr.
\n" ); document.write( "qw is perpendicular to sr, therefore angle rwq is 90 degrees.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"$$$\"
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "your solution is that x = 7.05453658 which is the same as x = sqrt(93.5304/(2*sin(70)))\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );