document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118980>Question 1118980</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The figure shows a right angled triangle where angle ACB=90°. Given that AB=(2x+1)cm, BC=2x cm and AC=(x-5) cm, <BR>\n" );
document.write( "1) write down an equation in X,<BR>\n" );
document.write( "2) find the value of X,<BR>\n" );
document.write( "3) find the area of triangle ABC. </SPAN>\n" );
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document.write( "The right angle is at C, so AB is the hypotenuse.  Then the Pythagorean Theorem says<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2%2B%28x-5%29%5E2+=+%282x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%282x%29%5E2%2B%28x-5%29%5E2+=+%282x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2Bx%5E2-10x%2B25+=+4x%5E2%2B4x%2B1 ALIGN=MIDDLE  ALT=\"4x%5E2%2Bx%5E2-10x%2B25+=+4x%5E2%2B4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-14x%2B24+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-14x%2B24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29%28x-2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-12%29%28x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x = 12  or  x = 2<br><BR>\n" );
document.write( "However, the solution x=2 gives a negative value for the length of one side of the triangle, so we choose the solution x=12.  Then the sides of the triangle are<BR>\n" );
document.write( "2x=24; x-5=7; 2x+1 = 25<br><BR>\n" );
document.write( "The area of a right triangle is one-half the product of the lengths of the legs:<BR>\n" );
document.write( "area = (1/2)(24)(7) = 84 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );