Question

in traingle ABC,DE parallel BC and AD/DB=3/5 and AE=4.5cm thenEC=​

Answer 1

Concept used:

Here, to solve this question use the concept of Thales Theorem or commonly referred to as Basic Proportionality Theorem (BPT). It states that if a line is drawn parallel to 1 side of a triangle to intersect the other 2 sides, then the other 2 sides are divided in the same ratio.

Solution:

(refer attachment)

• DE || BC
• AD/DB = 3/5
• AE = 4.5 cm

By BPT,

$\bf{\dfrac{AD}{DB} = \dfrac{AE}{EC} }$

$\implies \sf{ \dfrac{3}{5} = \dfrac{4.5}{EC} }$

$\implies \sf{3EC = 4.5 \times 5}$

$\implies \sf{EC = \dfrac{4.5 \times 5}{3} }$

$\implies \sf{EC = \dfrac{22.5}{3} }$

$\implies \sf{EC = 7.5 \: cm}$

∴ EC = 7.5 cm