document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48653>Question 48653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here are a few problems that were given as a summer test in preparation for AP Calculus.  I would appreciate it if I could recive soem help. The test is due tommorrow.  Thank you in advance for your help.\r<BR>\n" );
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document.write( "2. The three sides of a triangle are 9 inches, 11 inches, and 12 inches.  Joining the midpoints of the sides of the original triangle forms a new triangle.  Find the perimeter of the new triangle.\r<BR>\n" );
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document.write( "7. The hypotenuse of a right triangle is 15 inches, and the altitude upon the hypotenuse is 6 inches. Find the segme, ts of the hypotenuse.\r<BR>\n" );
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document.write( "8. A chord AB is 12 inches; E is its midpoint.  Another chord, CD, 13 inches in length, cuts AB at E. Find CE and ED.\r<BR>\n" );
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document.write( "14. Find the circumference of a circle if an inscribed angle of 18 degrees intercepts an arc 6 inches long.\r<BR>\n" );
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document.write( "Thanks agian </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32202 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=32202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2. The three sides of a triangle are 9 inches, 11 inches, and 12 inches. Joining the midpoints of the sides of the original triangle forms a new triangle. Find the perimeter of the new triangle.<BR>\n" );
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document.write( "Draw the picture.<BR>\n" );
document.write( "Notice the three parallelograms you formby connecting the mid-points.<BR>\n" );
document.write( "Each of the sides of the inner triangle is half of one of the outside sides.<BR>\n" );
document.write( "Perimeter = 6+4.5+5.5=16<BR>\n" );
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document.write( "7. The hypotenuse of a right triangle is 15 inches, and the altitude upon the hypotenuse is 6 inches. Find the segme, ts of the hypotenuse.<BR>\n" );
document.write( "Draw the picture.<BR>\n" );
document.write( "The antitude forms two similar triangles.<BR>\n" );
document.write( "The hypotenuse of the original triangle has two pieces: x and 15-x.<BR>\n" );
document.write( "PROPORTION:<BR>\n" );
document.write( "x/6=6/(15-x) <BR>\n" );
document.write( "15x-x^2=36<BR>\n" );
document.write( "x^2-15x+36=0<BR>\n" );
document.write( "(x-3)(x-12)=0<BR>\n" );
document.write( "x=3 inches ; 15-x=12 inches<BR>\n" );
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document.write( "8. A chord AB is 12 inches; E is its midpoint. Another chord, CD, 13 inches in length, cuts AB at E. Find CE and ED. <BR>\n" );
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document.write( "Draw the picture.<BR>\n" );
document.write( "You have formed two similar triangles because angle C and angle B <BR>\n" );
document.write( "intercept the same arc, so are equal. Also angle A and angle D intercept<BR>\n" );
document.write( "the same are, so are equal.  And the vertical angles at E are equal.<BR>\n" );
document.write( "So the triangles are similar.<BR>\n" );
document.write( "Let CE=x, then ED = 13-x.<BR>\n" );
document.write( "AE = 6 = EB<BR>\n" );
document.write( "Proportion:<BR>\n" );
document.write( "x/6 = 6/13-x<BR>\n" );
document.write( "13x-x^2=36<BR>\n" );
document.write( "x^2-13x+36=0<BR>\n" );
document.write( "(x-9)(x-4)=0<BR>\n" );
document.write( "x=9 then 13-x=4 or vice versa<BR>\n" );
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document.write( "14. Find the circumference of a circle if an inscribed angle of 18 degrees intercepts an arc 6 inches long. <BR>\n" );
document.write( "PROPORTION:<BR>\n" );
document.write( "circumference/6 = 360 degrees/ 18 degrees<BR>\n" );
document.write( "circum = 6(360/18)= 120 inches<BR>\n" );
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document.write( "Cheers<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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