Question

In ∆ ABC, DE ∥ BC. If AD =3cm, DB=4cm and AE=6cm, then EC is​

Answer 1

Given:

• AD = 3 cm
• BD = 4 cm
• AE =6 cm

To find:

☞ EC = ?

Method:

The Concept of Basic Proportionality theorem or Thales Theorem is used here.

It states that → when a line is drawn parallel to a side of a triangle, then the other 2 sides of the triangle gets divided in the same ratio.

Using the above theorem,

$\boxed{\sf{\dfrac{AD}{DB} = \dfrac{AE}{EC}}}$

$\\\\\Rightarrow \: \sf{\dfrac{3}{4} = \dfrac{6}{EC}}$

$\\\\\rm{On \: Cross \: Multiplication,}$

$\\\\\Rightarrow \sf{3 \times EC= 6 \times 4}$

$\\\\\Rightarrow \sf{EC=\dfrac{6 \times 4}{3}}$

$\\\\\therefore \boxed{\underline{\bf{EC = 8 \: cm}}}$

Answer 2

Step-by-step explanation:

Given:

DE || BC

AD = 3 cm

DB = 4 cm

AE = 6 cm

To find:

EC = ?

By the BPT theorem we can solve this problem...

BPT theorem states that:

when a line is drawn parallel to the base of the triangle, the other two sides of the triangle gets divided in the same ratio..

So,

$\frac{ad}{db} = \frac{ae}{ec}$

$\frac{3}{4 } = \frac{6}{ec}$

by cross multiplication;

$3 \times ec = 6 \times 4$

$ec = \frac{6 + 4}{3}$

$ec = 2 \times 4$

$ec = 8cm$

Therefore EC = 8 cm...