Alength of rope is stretched between the top edge of a building and a stake in the ground. the rope also touches a tree halfway between the stake and the building. if the building is 36 feet tall, how tall is the tree?

The answer is 18 ft.

x - the height of the building.
x1 - the height of the tree.
y - the distance between the building and the stake.
y1 - the distance between the tree and the stake.
 
x = 36 ft
x1 = ?
y = 1
y1 = 0.5 (because it is halfway between the stake and the building, which is y)

By similar triangles:
x : x1 = y : y1
36 : x1 = 1 : 0.5
x1 = 36 * 0.5 : 1
x1 = 18 ft

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