Question

If CD is a median of $\Delta$ABC, then find the ratio of Area $\left(\Delta ADC\right)$ to Area $\left(\Delta CDB\right)$

• A. 1:1
• B. 1:2
• C. 2:1
• D. 1:3

Answer 1

The correct option is A 1:1

In $\Delta$ABC, CD is the median. So, AD = DB. We have learned that any two triangles, even with equal base, if not common and between same parallel lines will also have equal area.

In the figure shown, CD is median. This means that AD = BD (Bases of $\Delta$ADC and $\Delta$DCB are equal in length)

Another point to note here is that CE is the height of both $\Delta$ADC and $\Delta$DCB corresponding to AD and BD respectively.

So, Area $\left(\Delta ADC\right)$ = Area $\left(\Delta DCB\right)$

This is more generally stated as

The median of any triangle divides it into two triangles with equal area.