Question

In A ABC, D and E are points AC and BC respectively such that DE DE || AB. If AD = 2x, BE = 2x – 1, CD = x + 1 and CE = x - 1, then find the value of x

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

AB AD = AC AE = BC DE

⇒AB AD = AC AE

⇒128 = AC 12

⇒8AC=12×12

⇒8AC=144

⇒AC=8

144

=18

Now, CE=AC−AE=18−12=6 cm

Hence, CE=6 cm