Question

In equilateral ΔABC, AD, BE, and CF are medians. If FO = 4, then AO =

Answer 1

Answer: 8

Explanation:

The medians intersect at point O. That intersection is called the centroid.

A, B, and C are the vertices.

D, E, and F are the sides.

The ratio of the lengths from a vertex to the centroid and a side to a the centroid is 2:1.

Also, since this is an equilateral triangle, then the lengths of the sides to the centroid are congruent (equal). Similarly, lengths of the vertices to the centroid are congruent (equal).

If FO is 4, then DO = 4

If DO = 4, then AO is 2(4) = 8

Answer 2

Answer:8

Explanation:

We know that in an equilateral triangle all medians are equal.

Here O is the centroid of the triangle, means O is the point where the three medians meet

And we know that centroid divides the median in the ratio 1:2

Here , since medians are equal , the respective divided parts must be equal.

We know FO is the line segment from centoid to the side AB at point F.

And FO = 4

And AO is the line segment from the centroid to the vertex A.

So AO and FO must be in the ratio 2:1

i.e. AO = 2FO

i.e. AO = 2*4

i.e. AO = 8

Hope it helps!!!