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?
(1 point)
80 ft
20 ft
10 ft
18 ft
Let's say the height of the tree is h ft.
Since the rope touches the top of the building, the total length of the rope is 40 ft + h ft + h ft = 40 + 2h ft.
Since the rope also touches the tree, the total length of the rope is half of the distance between the stake and the building plus half of the distance between the stake and the tree. These are both equal to h ft.
So, 40 + 2h ft = h ft + h ft.
⇒ 40 + 2h ft = 2h ft.
⇒ 40 = h ft.
Therefore, the height of the tree is 40 ft.
The correct option is 40 ft.