Math, asked by ashishshukla9541, 9 months ago

In Δ ABC, E is the mid-point of median AD such that BE produced meets AC at F. If AC = 10.5 cm, then AF =
A. 3 cm
B. 3.5 cm
C. 2.5 cm
D. 5 cm

Answers

Answered by nikitasingh79
10

Given : In Δ ABC, E is the mid-point of median AD such that BE produced meets AC at F and AC = 10.5 cm.

 

To find : The value of AF  

Construct : Draw DM || EF.

 

Proof :  

In ∆ABC,  

E is mid point of median AD

We have,  AC = 10.5 cm

∵ E is mid point of AD so F is mid point of AM

[By converse of mid point theorem]

∴ AF = FM ……………………(1)

 

In ∆BFC,D is the mid point of BC

EF || DM

G is the mid point of CF.

[By converse of mid point theorem]

So, FM = MC ………………….(2)

From eq (1) & (2),

AF = FM = MC……………..(3)

AC = AF + MC + FM

AC =  AF + AF + AF  

[From eq (3) ]

AC = 3AF

AF = AC/3

AF = ⅓ × 10.5  

AF = 3.5 cm

Hence , AF is 3.5 cm.

Among the given options option (B) 3.5 cm is correct.  

HOPE THIS ANSWER WILL HELP YOU…..

 

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Attachments:
Answered by Anonymous
2

Answer:

Step-by-step explanation:

In ∆ABC,  

E is mid point of median AD

We have,  AC = 10.5 cm

∵ E is mid point of AD so F is mid point of AM

[By converse of mid point theorem]

∴ AF = FM ……………………(1)

 

In ∆BFC,D is the mid point of BC

EF || DM

G is the mid point of CF.

[By converse of mid point theorem]

So, FM = MC ………………….(2)

From eq (1) & (2),

AF = FM = MC……………..(3)

AC = AF + MC + FM

AC =  AF + AF + AF  

[From eq (3) ]

AC = 3AF

AF = AC/3

AF = ⅓ × 10.5  

AF = 3.5 cm

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