Question

In triangle abc, d and e are the points on AB and AC such that DE ||BC if AD :DB =1:2 then DE:BC

Answer 1

Answer:

DE :BC=1:3

Step-by-step explanation:

since ∆ABC and ∆ADE are similar

given AD:DB =1:2

AD: AB =1:1+2=1:3

Answer 2

Answer:

1:3 is the required ratio of DE :BC .

Step-by-step explanation:

Explanation:

Given , ABC is a triangle  in which d and e are the points on AB and AC .

DE || BC  and AD : DB = $\frac{1}{2}$ .

Step 1:

According to the Basic Proportionality Theorem, if a line is drawn parallel to one side of a triangle and the other two sides are placed at distinct positions, the ratio of the other two sides will remain the same.

So, from the question we have , DE||BC .

⇒$\frac{AD}{DB} = \frac{AE}{EC}$  = $\frac{1}{2}$

And also ,

$\frac{AD}{AB} = \frac{AE}{AC}= \frac{DE}{BC}$          [corresponding side are proportional ]

⇒$\frac{AD}{AD +DB} = \frac{AE}{AE+EC} = \frac{DE}{BC}$

⇒ $\frac{1}{1+2}$ = $\frac{DE}{BC}$

⇒$\frac{DE}{BC} = \frac{1}{3}$

Final answer :

Hence , the ratio of DE:BC is 1 :3 .

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