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A length of a rope is is stretched between the top edge of a building and a stake in the ground. The head of the steak is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the tree is 38 feet tall, how tall is the building?
1: 38ft
2: 19ft
3: 76ft
4: 57ft

A length of a rope is is stretched between the top edge of a building and a stake in the ground. The head of the steak is at ground level. The rope also touches class=

Answer :

The building is 76 feet tall. Notice that there's a pair of similar triangles in this diagram: The top of the building, root of the building, and the stake form triangle 1. The top of the tree, root of the tree, and the stake form triangle 2. Since the root of the tree is half way between stake and building, the proportionality between the triangles is 2. Therefore, the building is twice as tall as the tree. 38*2=76.

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