February 2026 Problem of the Month

In triangle ABC, point D lies on side BC such that
𝐵𝐷 = 4 cm and 𝐷𝐶 = 6 cm.

Point E lies on side AC so that side DE is parallel to side AB.

If AC = 15 cm, find the length of AE.

Solution to the Problem:

Here is the solution:

AE = 6 cm.

△ABC ∼ △EDC by AAA (they share angle C and there are two pairs of corresponding angles).
So, the corresponding sides must be proportional:

DC / BC = EC / AC
6/10 = x/15 so x = 9 cm and therefore, EC = 9 cm.
So, AE = AC - EC = 15 - 9 = 6 cm.