Math, asked by BrainlyHelper, 1 year ago

In a ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC.
(i) If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If AD/DB = 3/4 and AC = 15 cm, find AE.
(iii) If ADDB=2/3 and AC = 18 cm, find AE.

Answers

Answered by nikitasingh79
35

BASIC PROPORTIONALITY THEOREM (BPT) :  

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

SOLUTION :  

1) Given : Δ ABC &  DE || BC ,

AD = 6 cm, DB = 9 cm and AE = 8 cm.

Let EC =x cm

So, AD/DB=AE/ EC

[By using basic proportionality  Theorem]

6/ 9 = 8/x

6x = 9 × 8

6x = 72 cm

x = 72/6 cm

x = 12 cm

AC = AE + EC

AC =  8 + 12

AC = 20 cm

Hence, the length of AC is 20 cm.

2) Given : Δ ABC &  DE || BC , AD/BD = 3/4 and AC = 15 cm

Let, AE = x cm

EC = AC - AE

EC = 15 - x

So, AD/DB=AE/ EC

[By using basic proportionality  Theorem]

Then, 3/4=x/15–x

3(15 - x) = 4x

45 -  3x = 4x

-3x - 4x =  - 45

7x = 45

x = 45/7

x = 6.43 cm

Hence, the length of AE is 6.43 cm.

3)Given : Δ ABC &  DE || BC ,AD/BD = ⅔ and AC = 18 cm

Let, AE = x cm

EC = AC - AE

EC = 18 - x

So, AD/DB = AE/ EC

[By using basic proportionality  Theorem]

Then, 2/3=x/18 - x

3x = 2(18 - x)

3x = 36 – 2x

3x + 2x = 36

5x = 36 cm

x = 36/5 cm

x = 7.2 cm

Hence, the length of AE is 7.2 cm

HOPE THIS ANSWER WILL HELP YOU...

Answered by aakash11300
4
sol_
(1) In triangleABC
DEparallel toBC
so,by Thales'Theorem
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