Question

in the given figure ef is parallel to ad and Ed is parallel to AC if bf =2cm fd =3cm and be =4cm find the value of bc

Answer 1

here is ur answer .........

Answer 2

The value of BC is 12.5 cm.

Step-by-step explanation:

Given:

EF || AD

ED || AC

BF= 2 cm

FD = 3 cm

BE = 4 cm

TO Find:

BC = ?

Solution:

Basic Proportionality Theorem:

Basic Proportionality Theorem states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

In Δ ABD,

EF || AD

$\dfrac{BF}{FD}= \dfrac{BE}{EA}$......Basic Proportionality Theorem

Substituting the values we get

$\dfrac{2}{3}= \dfrac{4}{EA}\\\\EA = 6\ cm$

Now, In Δ ABC,

ED || AC

$\dfrac{BD}{DC}= \dfrac{BE}{EA}$......Basic Proportionality Theorem

Substituting the values we get

$\dfrac{5}{DC}= \dfrac{4}{6}\\\\DC = 7.5\ cm$

Now For BC,

$BC=BF+FD+DC=2+3+7.5=12.5$

The value of BC is 12.5 cm.