document.write( "Question 531229: An isosceles trapezoid has a perimeter of 51 kilometers. Its shorter base measures 7 kilometers and its longer base measures 14 kilometers. The two remaining sides have the same length; what is that length? \n" ); document.write( "
Algebra.Com's Answer #350374 by shivang jindal(3)\"\" \"About 
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Solution:
\n" ); document.write( "Let OA = a
\n" ); document.write( " OB = b,
\n" ); document.write( " OC = c,
\n" ); document.write( "OD = d,
\n" ); document.write( " OE = e,
\n" ); document.write( " OF = f,
\n" ); document.write( " [OAB] =x,
\n" ); document.write( " [OCD] = y,
\n" ); document.write( "[OEF] = z,
\n" ); document.write( " [ODE] = u,
\n" ); document.write( "[OFA] = v
\n" ); document.write( "[OBC]= w.
\n" ); document.write( "We are given that v^2 = zx, w^2 = xy and we have to prove that u^2 =yz.
\n" ); document.write( "Since∠AOB =∠DOE, we have
\n" ); document.write( "u\x =(1/2 de sin∠DOE)/(1/2 ab sin∠AOB)= de/ab\r
\n" ); document.write( "\n" ); document.write( "Similarly, we obtain
\n" ); document.write( "v/y =fa/cd
\n" ); document.write( "w/z =bc/ef
\n" ); document.write( "Multiplying, these three equalities, we get uvw =xyz. Hence
\n" ); document.write( "x^2 * y^2 * z^2 =u^2*v^2*w^2 =u^2 (zx)(xy).
\n" ); document.write( "This gives u^2=yz, as desired.
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