The ramp shown below is used to move crates of fruit to loading docks of different heights. When the horizontal distance AB is 12 meters, the height of the loading dock, BC, is 4 meters. What is the height of the loading dock DE?
A. 12m
B. 8m
C. 9m
D. 15m
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To solve this problem, we can use the concept of similar triangles. Similar triangles have the same shape but not necessarily the same size.
In this case, we have two similar right triangles: triangle ABC and triangle DEC. The corresponding sides of these triangles are proportional.
We know that AB is 12 meters and BC is 4 meters. To find the height of the loading dock DE, we can set up a proportion:
AB/BC = DE/EC
Plugging in the known values, we get:
12/4 = DE/EC
Simplifying the fraction, we have:
3 = DE/EC
Since we are looking for the height of the loading dock DE, we can rewrite the equation as:
DE = 3 * EC
Now, we need to find the value of EC. We can do this by subtracting the height of the loading dock BC from the height of the ramp AB:
EC = BC - AB
Plugging in the values, we get:
EC = 4 - 12
EC = -8
Now, we can substitute the value of EC back into the DE equation:
DE = 3 * (-8)
DE = -24
Since distances cannot be negative, we made a mistake somewhere in our calculations. Let's check our work.
It seems there was a mistake in finding the value of EC. We should subtract the height of BC from the height of AB, not the other way around.
EC = AB - BC
EC = 12 - 4
EC = 8
Now, we can calculate DE again:
DE = 3 * EC
DE = 3 * 8
DE = 24
Therefore, the height of the loading dock DE is 24 meters.
The correct answer would be D. 15m
Sorry for the confusion, but my answer is 24 meters, not 9 meters.