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In Δ ABC , E ...

Question

In $Δ A B C$ , E is a point on AB, G and D are two points on BC such that EG is parallel to AD and ED is parallel to AC. Find the value of BC if BG = 4cm, GD = 6cm, and BE = 8cm.

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Solution

The correct option is C

Clearly, $(Δ G B E) \sim Δ D B A)$ and $(Δ D B E) \sim (Δ C B A)$
therefore we have, $(\frac{B E}{B A}) = (\frac{B G}{B D})$
$\frac{8}{B A} = \frac{4}{10}$
BA = 20
also, $(\frac{B E}{B A}) = (\frac{B D}{B C})$
BC = 25cm

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Similar questions

Q. In

∠ A B C

E

is a point on

A B

F

and

D

are two points on

B C

such that

E F

parallel to

A D

and

E D

parallel to

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B F = 4

cm,

F D = 6

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B E = 8

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B C =

____

In triangle ABC, DE is parallel to BC; where D and E are the points on AB and AC respectively. Also, if AD = 12 cm, BD = 24 cm and BC = 8 cm, the length of DE is

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and

A C

respectively such that

D E | | B C

.
If

A D = 2 c m, A B = 6 c m

and

A C = 9 c m

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Q. In a

Δ A B C

D

and

E

are points on the sides

A B

and

A C

respectively such that

D E | | B C

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and

A E = 12 c m

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Q. In a

Δ A B C

D

and

E

are points on the sides

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In ΔABC, E is a point on AB, G and D are two points on BC such that EG is parallel to AD and ED is parallel to AC. Find the value of BC if BG = 4cm, GD = 6cm, and BE = 8cm.

The correct option is C Clearly, (ΔGBE)∼ΔDBA) and (ΔDBE)∼(ΔCBA) therefore we have, (BEBA)=(BGBD) 8BA=410 BA = 20 also, (BEBA)=(BDBC) BC = 25cm

In $Δ A B C$ , E is a point on AB, G and D are two points on BC such that EG is parallel to AD and ED is parallel to AC. Find the value of BC if BG = 4cm, GD = 6cm, and BE = 8cm.

The correct option is C

Clearly, $(Δ G B E) \sim Δ D B A)$ and $(Δ D B E) \sim (Δ C B A)$
therefore we have, $(\frac{B E}{B A}) = (\frac{B G}{B D})$
$\frac{8}{B A} = \frac{4}{10}$
BA = 20
also, $(\frac{B E}{B A}) = (\frac{B D}{B C})$
BC = 25cm