Question

QUESTION 6 Triangle D E F is shown. Lines are drawn from each point to the opposite side and intersect at point G. Line segments D C, E B, and F A are formed and cut each side into 2 equal parts. If FG = 28 cm, what is AG? A. 14 cm B. 28 cm C. 7 cm D. 42 cm

Answer 1

The value of AG from triangle DEF is 14 cm. option A

What is AG?

As we can see in the attached figure that G is the point at which the three medians of the triangle meet, that is, the centroid

And, according to the property of the centroid, it divides the medians in ratio 2:1

So,

FG: AG = 2 : 1

Since the FG is 28 cm

28 : AG = 2: 1

28/AG = 2/1

cross product

28 × 1 = AG × 2

28 = 2AG

Divide both sides by 2

AG = 28/2

AG = 14 cm

Therefore, AG would be half of FG which equals 14 cm