document.write( "Question 1138478: Two dogs start, at the same time, from points
\n" ); document.write( "C and D on a beach and run toward their owner, who is posi-
\n" ); document.write( "tioned at point X. If the dogs run at the same rate and reach their
\n" ); document.write( "owner at the same instant, what is the distance AX? See the dia-
\n" ); document.write( "gram below. Note: Angle A and Angle B are right angles.\r
\n" ); document.write( "\n" ); document.write( "Here is the 3D figure: https://i.imgur.com/LIrDz5V.png \n" ); document.write( "

Algebra.Com's Answer #756272 by ikleyn(52787) $\"\"$ $\"About$

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

\r\n" );
document.write( "(1)  From the condition, the segments CX and DX have the same length \r\n" );
document.write( "\r\n" );
document.write( "        (thanks to the dogs, who proved it by covering these distances at the same time, running with the same rate).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  The right angled triangles CAX and DBX have pairs of congruent angles \r\n" );
document.write( "\r\n" );
document.write( "         C ~ DXB  and  D ~ CXA.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Hence, the triangles CAX and DBX are congruent.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3)  It implies that corresponding sides of these triangles are congruent:\r\n" );
document.write( "\r\n" );
document.write( "        |AX| = |BD| = 40 yd;   |BX| = |AC| = 60 yd.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  |AX| = 40 yd;   |BX| = 60 yd.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.   |AX| + |BX| = 40 + 60 = 100,  in accordance with the figure.\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" );