In triangle ABC, line DE is drawn parallel to BC, meeting AB at D and AC at E, with AD:DB = 1:2. Since DE is parallel to BC, triangle ADE ~ triangle ABC. Find the ratio area(ADE) : area(ABC).

Question

Accepted Answer

1:9. AD:DB = 1:2 means AD:AB = 1:3. By BPT, triangle ADE ~ triangle ABC with ratio 1/3. Area ratio = (1/3 )^2 = 1:9.

In triangle ABC, line DE is drawn parallel to BC, meeting AB at D and AC at E, with AD:DB = 1:2.
Since DE is parallel to BC, triangle ADE ~ triangle ABC.
Find the ratio area(ADE) : area(ABC).

Step-by-Step Solution

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More Class 10 Areas of Similar Triangles practice

In triangle ABC, line DE is drawn parallel to BC, meeting AB at D and AC at E, with AD:DB = 1:2.Since DE is parallel to BC, triangle ADE ~ triangle ABC.Find the ratio area(ADE) : area(ABC).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

In triangle ABC, line DE is drawn parallel to BC, meeting AB at D and AC at E, with AD:DB = 1:2.
Since DE is parallel to BC, triangle ADE ~ triangle ABC.
Find the ratio area(ADE) : area(ABC).