Question
Don't forget to use your reference chart on the test! It can be found here Unit 6 Reference Chart
stake
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)
A 20 ft
B 80 ft
C 18 ft
D 10 ft
stake
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)
A 20 ft
B 80 ft
C 18 ft
D 10 ft
Answers
GPT 3.5
Let's call the height of the tree "h".
Since the tree is growing halfway between the stake and the building, the distance from the stake to the tree is the same as the distance from the tree to the building.
Therefore, we can divide the rope into two equal parts:
Segment 1: From the stake to the tree
Segment 2: From the tree to the building
Let's call the length of each segment "x".
Since the building is 40 ft tall, segment 2 has a length of 40 ft.
Segment 1 + Segment 2 = Length of the rope
x + 40 ft = Length of the rope
Since the rope is stretched between the top edge of the building and the stake, the length of the rope is equal to the height of the building.
Therefore, we can write the equation as:
x + 40 ft = 40 ft
Now, let's solve for x:
x + 40 ft - 40 ft = 40 ft - 40 ft
x = 0 ft
This means that segment 1 has a length of 0 ft. Since the tree is growing halfway between the stake and the building, its height is equal to the length of segment 1.
Therefore, the height of the tree is 0 ft.
D 10 ft
Since the tree is growing halfway between the stake and the building, the distance from the stake to the tree is the same as the distance from the tree to the building.
Therefore, we can divide the rope into two equal parts:
Segment 1: From the stake to the tree
Segment 2: From the tree to the building
Let's call the length of each segment "x".
Since the building is 40 ft tall, segment 2 has a length of 40 ft.
Segment 1 + Segment 2 = Length of the rope
x + 40 ft = Length of the rope
Since the rope is stretched between the top edge of the building and the stake, the length of the rope is equal to the height of the building.
Therefore, we can write the equation as:
x + 40 ft = 40 ft
Now, let's solve for x:
x + 40 ft - 40 ft = 40 ft - 40 ft
x = 0 ft
This means that segment 1 has a length of 0 ft. Since the tree is growing halfway between the stake and the building, its height is equal to the length of segment 1.
Therefore, the height of the tree is 0 ft.
D 10 ft