The diagram below shows a rectangular garden with walkways along the diagonals. A fountain is located at point F, which is the center of the park. Tara enters the park through the west gate and walks (3x + 2) yards to reach the fountain. Ursula enters the park through the east gate and walks (x + 10) yards to reach the same spot.

What is the approximate distance Ursula walks to reach the fountain from the east gate of the park?

Question

The diagram below shows a rectangular garden with walkways along the diagonals.  A fountain is located at point F, which is the center of the park. Tara enters the park through the west gate and walks (3x + 2) yards to reach the fountain. Ursula enters the park through the east gate and walks (x + 10) yards to reach the same spot. 
 

 
What is the approximate distance Ursula walks to reach the fountain from the east gate of the park?

anonymous · Answer

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directrix · Answer

F is the center of the rectangle and is the point of intersection of the diagonals. The diagonals of a rectangle bisect each other. The diagonals are also congruent.

So, 3x + 2 = x + 10

2x = 8
x = 4

directrix · Answer

x + 10 = 14 yards for Ursula to walk.

anonymous · Answer

Thanks! :D