A length of rope is stretched between the top edge of a building and a stake in the ground. The head of the stake is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the building is 40 ft tall, how tall is the tree?
18 ft
80 ft
20 ft
10 ft
Let's assume that the height of the tree is x ft.
Since the rope is stretched between the top edge of the building and the stake in the ground, the length of the rope is equal to the height of the building + the height of the tree.
Therefore, the length of the rope is 40 ft + x ft.
Since the rope also touches the tree that is growing halfway between the stake and the building, we can divide the length of the rope into two equal parts:
- The distance from the stake to the tree is x/2 ft.
- The distance from the tree to the top edge of the building is also x/2 ft.
Therefore, the total distance from the stake to the top edge of the building is x/2 ft + 40 ft.
Given that the rope is stretched between the stake (at ground level) and the top edge of the building, the total distance from the stake to the top edge of the building is equal to the length of the rope.
So, we have the equation: x/2 ft + 40 ft = 40 ft + x ft.
By simplifying the equation, we get x/2 ft = 40 ft.
Multiplying both sides of the equation by 2, we get x ft = 80 ft.
Therefore, the tree is 80 ft tall.
So, the correct answer is 80 ft.