Question

In triangle ABC,DE is parallel to BC and AD/DB =3/5 If AE =2.1 then find AC

Answer 1

3/5 = 2.1/X
X= 10.5/3
X= EC = 3.5
AC = AE + EC = 2.1 + 3.5 = 5.6

Answer 2

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 than the other two sides are divided in the same ratio.


Solution:

In ∆ABC , DE||BC

Let EC = x cm

AD/DB= AE/EC

[ By basic PROPORTIONALITY theorem]

3/5 = 2.1/x

3 EC = 2.1 × 5

EC =( 2.1× 5)/3

EC = .7 ×5 = 3.5

EC = 3.5 cm

AC = AE+EC

AC= 2.1+ 3.5= 5.6

AC = 5.6 cm

Hence, AC is = 5.6 cm

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Hope this will help you...