Question

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?

Answer 1

Answer:

9 m

Step-by-step explanation:

ΔABC and ΔADE are similar. That means:

the sides corresponding to each other are proportional.

We can set up ratio for two triangle and solve for DE.

AB corresponds to AD (AB + BD)

and

BC corresponds to DE

Now, lets setup a ratio:

$\frac{AB}{AD}=\frac{BC}{DE}\\\frac{AB}{AB+BD}=\frac{BC}{DE}$

Now we substitute the values known and solve for DE. Process is shown below:

$\frac{AB}{AB+BD}=\frac{BC}{DE}\\\frac{12}{12+15}=\frac{4}{DE}\\\frac{12}{27}=\frac{4}{DE}\\12DE=27*4\\12DE=108\\DE=\frac{108}{12}\\DE=9$

hence, the length of DE is 9 m