# Find the dimensions of a square

• Feb 25th 2010, 07:10 AM
nikie1o2
Find the dimensions of a square
A square walled city of unknown dimensions has four gates, one at the center of each side. A tree stands 20 m from the north gate. one must walk 14 m southward from the south gate and 1775m west before one can see the tree. what are the dimensions of the city?
• Feb 25th 2010, 12:28 PM
earboth
Quote:

Originally Posted by nikie1o2
A square walled city of unknown dimensions has four gates, one at the center of each side. A tree stands 20 m from the north gate. one must walk 14 m southward from the south gate and 1775m west before one can see the tree. what are the dimensions of the city?

1. Draw a sketch.

2. You are dealing with similar right triangles. Use proportions:

$\dfrac{20}{\frac12 x} = \dfrac{34+x}{1775}$

Solve for x.

Spoiler:
You should come out with x = 250 m. The negative solution of the equation isn't very plausible here.
• Feb 25th 2010, 01:33 PM
nikie1o2
The sketch was very helpful. thank you !