February 2026
Problem of the Month

Triangle Problem

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:

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.

Correctly solved by:

1. Davit Banana	Istanbul, Turkey
2. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
3. Kamal Lohia	Hisar, Haryana, India
4. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
5. Kelly Stubblefield	Mobile, Alabama, USA
6. Ivy Joseph	Pune, Maharashtra, India

Send any comments or questions to: David Pleacher