Given a triangle ABC and a point 'D' divides the side AB such that a triangle ADC is formed & AD/DB=1/3. If the area of the triangle ABC is r, then find the area of the triangle ADC in terms of r?

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- August 9th 2010, 08:30 AMsfspitfire23triangle and ratios
**Given a triangle ABC and a point 'D' divides the side AB such that a triangle ADC is formed & AD/DB=1/3. If the area of the triangle ABC is r, then find the area of the triangle ADC in terms of r?** - August 9th 2010, 08:49 AMskeeter
let AB = b be the base of triangle ABC and h = height from C to AB ...

area of triangle ABC = (1/2)bh = r

since AD = (1/4)b

area of triangle ADC = (1/2)(1/4)bh = (1/4)(1/2)bh = (1/4)r - August 9th 2010, 08:50 AMGoethe
AD/DB=1/3, so think of line AB as being divided into 4 equal segments, and that each of the three points dividing the line segments on AB have a straight line connecting to point C, creating 4 equal triangles within the triangle ABC, ADC being one of those

therefore, triangle ADC=(1/4)r