A length of a rope is stretched between the top edge of a building and a stake in the ground. The head of the stake is a ground level the rope also touches a tree that is growing halfway between the stake and the building if the building is 40 feet tall how tall is a tree?
1. 10 ft
2. 20 ft
3. 18 ft
4. 80 ft
The height of the tree is 20 feet.
To determine this, we can use the concept of similar triangles.
Let's assume the height of the tree is h feet.
Since the rope touches the tree halfway between the stake and the building, the distance between the stake and the tree is also 20 feet.
Now, we can form two right triangles - one with the building, the stake, and the rope, and the other with the tree, the stake, and the rope.
The height of the building is given as 40 feet, and the distance between the stake and the building is 20 feet.
Using the concept of similar triangles, we can set up the following proportion:
h/20 = 40/20
Simplifying this equation:
h/20 = 2
Cross-multiplying:
h = 2 * 20
h = 40
Therefore, the height of the tree is 40 feet.
Hence, the correct answer is option 2.