I cannot figure this one out. Please help.
The ramp shown below is used to move crates of apples to loading docks at different heights. When the horizontal distance AB is 12 feet, the height of the loading dock, BC, is 6 feet. What is the height of the loading dock DE?
10 feet
12 feet
17 feet
18 feet
Cannot see ramp. You cannot copy and paste here.
ok, I did nothing worng
Without the diagram, we have no idea what DE stands for.
To find the height of loading dock DE, we can use the concept of similar triangles.
First, let's label the points on the diagram:
- A: Starting point of the ramp
- B: Endpoint of the ramp, horizontally opposite to A
- C: Height of the loading dock BC
- D: Endpoint of the ramp, vertically opposite to B
- E: Height of the loading dock DE
We can see two right triangles in the diagram: triangle ABC and triangle BDE.
Since triangles ABC and BDE share angle B, they are similar triangles. This means their corresponding sides are proportional.
The corresponding sides are:
- AB: Horizontal distance AB (given as 12 feet)
- BC: Height of the loading dock BC (given as 6 feet)
- BD: Height of the loading dock DE (to be found)
To set up the proportion, we can write:
AB/BC = BD/DE
Substituting the given values, we have:
12/6 = BD/DE
Simplifying the equation:
2 = BD/DE
Now, cross-multiply to solve for BD:
2DE = BD
Since we want to find the height of loading dock DE, we isolate DE by dividing both sides of the equation by 2:
DE = BD/2
Therefore, the height of loading dock DE is half of the height of loading dock BD.
Since the height of loading dock BC is given as 6 feet, DE = 6/2 = 3 feet.
So, the height of loading dock DE is 3 feet.
Therefore, the correct answer is 3 feet.