Question

In triangle ABC , AB/AC is 4/3 and M is the midpoint of BC and E is a point on AB and F on AE such that AE/AF is 2/1...this also given that EF and AM intersect at G with GF is 72 cm and GE is x cm....then find x

Answer 1

In figure, in triangle ABC , AB/AC is 4/3 and M is the midpoint of BC and E is a point on AB and F on AE such that AE/AF is 2/1. Also given that EF and AM intersect at G.

Given,

AB / AC = 4 / 3

M is the midpoint of BC

E is a point on AB

F is a point on AE

AE / AF = 2 / 1

GF = 72 cm

Now, consider

AE / AB = 2 / 4 = 1/2

AF / AC = 1 / 3

Since, AE / AB  > AF / AC

as, 1/2 > 1/3

Therefore,

GE > GF

So, we have,

AE / EG = AF / GF

2 / EG = 1 / GF

GE = 2 GF

⇒ GE = 2 × 72

∴ GE = x = 144 cm