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AC and DE are two parallel streets. CD is a road at right angles joining the two streets. The post office is located on the road CD at point B.

Two triangles ABC and BDE are shown. The post office is shown at point B. Measure of angle ACB is 90 degrees and measure of angle BDE is 90 degrees. Distance BC is 8 miles and the distance BD is 4 miles. BE is 5 miles.

What is the distance between point A and the post office?

10 miles

17 miles

12 miles

9 miles

Question

I give out medals to whoever helps me!

AC and DE are two parallel streets. CD is a road at right angles joining the two streets. The post office is located on the road CD at point B.
 
Two triangles ABC and BDE are shown. The post office is shown at point B. Measure of angle ACB is 90 degrees and measure of angle BDE is 90 degrees. Distance BC is 8 miles and the distance BD is 4 miles. BE is 5 miles.
 
What is the distance between point A and the post office?

 10 miles

 17 miles

 12 miles

 9 miles

anonymous · Answer

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btaylor · Answer

The two triangles formed are similar. So, using the ratio BC:BD (8:4 --> 2:1), the ratio of AB:EB must be the same. AB/EB=2 --> AB/5=2 --> AB = 10 miles.

anonymous · Answer

I am definitely not good at this. haha you dont know how greatful I am. :)