Question

1. 1. If a Triangle ABC, D and E are points on the sides AB and AC respectively such that AD parallel to BC. If AD = 3.5 cm and DB = 2.0 cm and AE = 4.75 cm, find the length of AC.

Answer 1

Answer:

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that AD=8 cm, AB=12 cm and AE=12 cm.

Using the basic proportionality theorem, we have

ABAD=ACAE=BCDE⇒ABAD=ACAE⇒128=AC12⇒8AC=12×12⇒8AC=144⇒AC=8144=18

Now, CE=AC−AE=18−12=6 cm

Hence, CE=6 cm.