Question

3. In ∆ABC, DE || BC and AD = 4cm, AB = 9cm. AC = 13.5 cm then the value of EC is (a) 6 cm (b) 7.5 cm (c) 9 cm (d) none of these​

Answer 1

Triangle

Given:

In ΔABC , $DE||BC$ and

$AD=4cm\\AB=9cm\\AC=13.5 cm$

To find:

Value of EC

Explanation:

Basic proportionality theorem:

If a line is drawn parallel to  any one side of a triangle which intersects the other two sides in distinct points, then the other two sides are divided in the same ratio. It is also called Thales Theorem.

It is the concept of similar triangles.

If it is given that 2 triangles are similar then,

1. Corresponding angles of both the triangles are equal.
2. Corresponding sides of both the triangles are in some proportion.

$\frac{AD}{AB} =\frac{AE}{AC}$  (by basic proportionality theorem)

$=>\frac{4}{9} =\frac{AE}{13.5}$

$AE= 6cm$

and,

$EC=AC-AE$

$EC=13.5-6\\=>EC=7.5 cm$

Hence, the value of EC is 7.5 cm.

Answer 2

Value of EC= 7.5 cm, if in  ΔABC, DE II BC  and  AD = 4cm, AB = 9 cm, AC = 13.5 cm

Given : In ΔABC, DE II BC

AD = 4cm,  AB = 9 cm,  AC = 13.5 cm,

To Find : the value of EC  

a) 6 cm b) 7.5 cm c) 9 cm d) none​

Solution:

Thales Theorem / BPT ( Basic Proportionality Theorem)  

"if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio"

In ΔABC, DE II BC

=> AD/ DB  =  AE / EC

AD = 4 cm

AB = AD + DB   ( Segment Addition postulate)

=> 9 = 4 + DB

=> DB = 5 cm

4/ 5  =  AE/EC

=> AE  = 4EC/5

AE + EC  = AC   ( Segment Addition postulate)

4EC/5  + EC  = 13.5

=> 9EC = 5 * 13.5

=> EC = 5 * 1.5

=> EC = 7.5 cm

value of EC= 7.5 cm

Correct option is b) 7.5 cm

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