UPSC CDS Math Triangles Questions

In ΔABC, D is the mid-point of BC.
Therefore, AD is the median
Remember:
The median divides the triangle into two triangles of equal area.
∴ ar(ΔADB) = ar(ΔADC)......(1)
⇒ar(ΔABC) = 2ar(ΔADB).....(2)
In ΔABD, E is the mid-point of AD.
∴ BE is the median
⇒ar (ΔABE) = ar (ΔBED)
⇒ ar(ΔADB) = 2ar(ΔBED)....(3)
From (2) and (3), we have
ar (ΔABC) = 4ar (ΔBED)
Hence, statement 1 is correct.
From (1) and (3), we have
ar(ΔADC) = 2ar(ΔBED).
Hence, statement 2 is correct