In the accompanying diagram of triangle ABC side DE is parallel to AC. If BD is 8 and BA is 18, that is all on side d is the midpoint of BA and BC is 27 with the midpoint E what is the length of BE??
We cannot see your diagram.
To find the length of BE, we can use the concept of parallel lines and their corresponding sides.
In the given diagram, we have triangle ABC with side DE parallel to AC. We are also provided with the lengths of BD, BA, and BC.
First, let's identify the relationship between BD and DE. Since BD and DE are parallel, we can apply the property of corresponding sides.
Since D is the midpoint of BA, we can infer that AD = AB/2. Therefore, AD = 18/2 = 9.
Now, let's look at triangle AED. We know that DE is parallel to AC, which means triangle AED is similar to triangle ABC. This similarity allows us to set up the following proportion:
AD/AB = DE/BC
Plugging in the known values, we have:
9/18 = DE/27
Now, we can solve for DE:
DE = (9/18) * 27
DE = 13.5
Since E is the midpoint of BC, BE is half the length of BC. Therefore:
BE = BC/2
BE = 27/2
BE = 13.5
Hence, the length of BE is 13.5 units.