Question 1138478: Two dogs start, at the same time, from points
C and D on a beach and run toward their owner, who is posi-
tioned at point X. If the dogs run at the same rate and reach their
owner at the same instant, what is the distance AX? See the dia-
gram below. Note: Angle A and Angle B are right angles.
Here is the 3D figure: https://i.imgur.com/LIrDz5V.png
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
(1) From the condition, the segments CX and DX have the same length
(thanks to the dogs, who proved it by covering these distances at the same time, running with the same rate).
(2) The right angled triangles CAX and DBX have pairs of congruent angles
C ~ DXB and D ~ CXA.
Hence, the triangles CAX and DBX are congruent.
(3) It implies that corresponding sides of these triangles are congruent:
|AX| = |BD| = 40 yd; |BX| = |AC| = 60 yd.
ANSWER. |AX| = 40 yd; |BX| = 60 yd.
CHECK. |AX| + |BX| = 40 + 60 = 100, in accordance with the figure.
Solved.
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