document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254769>Question 254769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A rhombus with diagonals of lengths 18 and 30. What are the area???\r<BR>\n" );
document.write( "\n" );
document.write( "2. An isosceles triangle with sides of lengths 10, 10 and 12. what are the area??\r<BR>\n" );
document.write( "\n" );
document.write( "3.A rectangle has width represented by x and length 4x. if the area of the rectangle is 80. find the value of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187078 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=187078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. A rhombus with diagonals of lengths 18 and 30. What are the area??? <BR>\n" );
document.write( "2. An isosceles triangle with sides of lengths 10, 10 and 12. what are the area?? <BR>\n" );
document.write( "3.A rectangle has width represented by x and length 4x. if the area of the rectangle is 80. find the value of x?\r<BR>\n" );
document.write( "\n" );
document.write( "1) There is a theorem that says the area of a rhombus is equal to half the product of its diagonals. In this case area = (18*30)/2.\r<BR>\n" );
document.write( "\n" );
document.write( "2) If the triangle is ABC and AB = AC = 10 and AC = 12 then we can drop a perpenduclar from the vertex at B bisecting the side AC at point D and also the angle B (<B). \r<BR>\n" );
document.write( "\n" );
document.write( "We then have two congruent triangles ABD and CBD. BD = DC = 5. By the Pythagorean Teorem we know then that 10^2 = 5^2 + BD^2. \r<BR>\n" );
document.write( "\n" );
document.write( "So BD^2 = 75 = 5*sqrt(3). Since BD is the altitude of the triangle the area is (1/2)*12*(5*sqrt(3)) = 30*sqrt(3).\r<BR>\n" );
document.write( "\n" );
document.write( "3) Since the area is length times width we have:\r<BR>\n" );
document.write( "\n" );
document.write( "x*(4x) = 80<BR>\n" );
document.write( "4*x^2 = 80<BR>\n" );
document.write( "x^2 = 20<BR>\n" );
document.write( "x = sqrt(20) = sqrt(4*5) = 2*sqrt(5)  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );