Question

In the following figure, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm.

Answer 1

Given:

In triangle ABC, DE || BC.

AE = 1.8 cm, BD = 7.2 cm, CE = 5.4 cm.

Step-wise calculation:

1. By the Basic Proportionality (Thales) Theorem, since DE || BC, the segments on the other two sides are proportional:

`(AD)/(DB) = (AE)/(EC)`

2. Compute the ratio `(AE)/(EC) = 1.8/5.4`

= `1/3`

3. Therefore `AD = (AE)/(EC) xx DB`

= `1/3 xx 7.2` cm

= 2.4 cm