Question

in given figure DE||BC. if AD =3cm, DB=4cm and AE=6cm,then find EC

Answer 1

Answer:

EC = 8 cm

Step-by-step explanation:

DE  || BC

:. AD / AB = AE / EC

or,   3 / 4 = 6 / EC

    :.       EC = 8 cm

Answer 2

Given: in given figure DE||BC. if AD =3cm, DB=4cm and AE=6cm.

To find: EC

Solution:

The triangles ABC and ADE have a common angle ∠A. The ∠D is corresponding to ∠B and hence, they are equal. Similarly, ∠E and ∠C are equal. Thus, the triangles ABC and ADE are similar to each other by the AAA (Angle-Angle-Angle) postulate.

Now, the corresponding sides of similar triangles must be in proportion. According to the question, the length of AB is 7 cm, AD is 3 cm and AC is 6 cm. So, the length of AC can be found as follows.

$\frac{3}{7} = \frac{6}{AC}$

$AC = 14$

Hence, the length of EC can be calculated as follows.

$14 - 6 = 8 cm$

Therefore, EC is 8 cm.

Although a figure of your question is missing, you might be referring to the one attached.