Question

In the given figure, AD and CF are the medians of ΔABC intersecting at G. The length of GD can be equal to

• A. 4 cm
• B. 6.5 cm
• C. 4.5 cm
• D. 7 cm

Answer 1

The correct option is B 6.5 cm

The point of intersection of medians divides each median in the ratio 2 : 1.
∴ AG : GD = 2 : 1
Let, AG = 2k and GD = k.
⇒ AD = 2k + k = 3k
In a triangle, the sum of any two sides is always greater than the third side and the difference of any two sides is always less than the third side.
∴ In ΔAGC,
AC – GC < AG < AC + GC
⇒ 15 – 6 < AG < 15 + 6 (∵ AC = 15 cm and GC = 6 cm)
⇒ 9 < 2k < 21
⇒ 4.5 < k < 10.5 …..(i)
Similarly, in ΔADC,
AC – DC < AD < AC + DC
⇒ 15 – 5 < 3k < 15 + 5
⇒ 10 < 3k < 20
⇒ 3.33 < k < 6.66 …..(ii)
From (i) and (ii), we get
4.5 < k < 6.66
⇒ 4.5 < GD < 6.66
Hence, the correct answer is option (b).