Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

It is given that in a triangle ABC, a line from A to BC intersects BC at point D. If the ratio in which AD divides BC is given can we say anything about the ratio of areas of triangle ABD and triangle ADC ?

enter image description here

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

Yes we can find the ratio of the areas of the two triangles.
Area of triangle $ADC$=$$(AD*DC*Sin\theta)\over2$$ Area of triangle $ABD$=$$(AD*DB*Sin(180-\theta))\over2$$ [$\theta$ is the angle $ADC$]

Divide these two equations and use the ratio you have to get the answer.

share|improve this answer
1  
So basically the areas are divided in the ratio of the lengths of AD and DB as the rest of the terms will cancel. –  Suy Oct 10 '13 at 18:38
1  
Yes that is true. –  Rnjai Lamba Oct 10 '13 at 18:39
1  
More simply, this results from the fact that both triangles have the same altitude –  Bill Kleinhans Oct 10 '13 at 20:42
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.