document.write( "Question 1149603: Triangle ABC below is isosceles, with AB=AC. A square is inscribed in the triangle, with edges 26cm, and BC=42cm. Find the area, in cm2, of triangle ADE. \r
\n" ); document.write( "\n" ); document.write( "Diagram: https://imgur.com/a/uFHAhYO \n" ); document.write( "

Algebra.Com's Answer #770935 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Triangles ADE and ABC are similar, and the similarity coefficient is   = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let x be the altitude of the triangle ADE;  then the altitude of the triangle ABC is   (x+26) centimeters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The ratio of altitudes is the same\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    21x = 13*(x+26)\r\n" );
document.write( "\r\n" );
document.write( "    21x = 13x + 13*26\r\n" );
document.write( "\r\n" );
document.write( "    21x - 13x = 338\r\n" );
document.write( "\r\n" );
document.write( "     8x       = 338\r\n" );
document.write( "\r\n" );
document.write( "      x       = 338/8 = 42.25  cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the height of the triangle ADE is  42.25 cm;  then its area is   = 549.25 cm^2.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );