Mathematics

Mathematics

Problem

In

\triangle ABC

, point

D

lies on

AB

and point

E

on

AC

such that

DE\parallel BC

. Inside

\triangle ADE

, point

F

is on

AD

and point

G

on

AE

with

FG\parallel DE

. If

AD = 5\,\text{cm}

,

DB = 10\,\text{cm}

,

AF = 3\,\text{cm}

,

FD = 2\,\text{cm}

and

AG = 6\,\text{cm}

, determine the length of

AC

. a)

24\ \text{cm}

b)

30\ \text{cm}

c)

20\ \text{cm}

d)

40\ \text{cm}

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