document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977682>Question 977682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi tutors, can u help me answer this question? thanks\r<BR>\n" );
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document.write( "There is a point X inside a square PQRS such that PX = 1, QX = 2 and triangles PXQ and PXS are congruent. What is the area, in square units, of the square?\r<BR>\n" );
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document.write( "A.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281+%2B+sqrt%28+7+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+%281+%2B+sqrt%28+7+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B. 4<BR>\n" );
document.write( "C. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+-+sqrt%28+7+%29+ ALIGN=MIDDLE  ALT=\"+4+-+sqrt%28+7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+%2B+sqrt%28+7+%29+ ALIGN=MIDDLE  ALT=\"+4+%2B+sqrt%28+7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "E. 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599380 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "In order for triangles PXQ and PXS to be congruent, angles SPX and QPX must be congruent, which is to say they bisect the right angle vertex P.  Construct a segment XY that is parallel to side PS and is perpendicular to PQ, intersecting PQ at Y.\r<BR>\n" );
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document.write( "Triangle PXY is then an isosceles right triangle with hypotenuse 1.  And therefore segments PY and XY both measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{\frac{1}{2}}\">\r<BR>\n" );
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document.write( "Now consider triangle QXY which is a right triangle with hypotenuse 2 and leg that measures <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{\frac{1}{2}}\">.  From this information and the Pythagorean Theorem, you can calculate the measure of QY.\r<BR>\n" );
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document.write( "The measure of the side of the square is PY + QY.  Square this value to find the area of your square.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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