In a triangle ABC, DE is parallel to BC. If AD/DB = 2/3 and AC = 18 cm, then find AE.

In triangle ABC, we have a line segment DE that is parallel to side BC. Given that the ratio of AD to DB is 2:3, we can use this information to find the length of AE.

Understanding the Ratios

The ratio AD:DB = 2:3 means that for every 2 parts of AD, there are 3 parts of DB. This indicates that the entire segment AB can be divided into 5 equal parts (2 + 3).

Calculating the Lengths

Let the length of AD be 2x and the length of DB be 3x. Therefore, the total length of AB is:

• AB = AD + DB = 2x + 3x = 5x

Using Similar Triangles

Since DE is parallel to BC, triangles ADE and ABC are similar. This gives us the following ratio:

• AD/AB = AE/AC

Substituting the Values

We know AC = 18 cm, and we can express AB in terms of x:

• AD/AB = (2x)/(5x) = 2/5
• AE/18 = 2/5

Finding AE

Now, we can solve for AE:

• AE = (2/5) * 18
• AE = 36/5
• AE = 7.2 cm

Thus, the length of AE is 7.2 cm.