Question

Please answer asap. I need it

Answer 1

BG = 5

GE = 10

Explanation:

The centroid of a triangle is the point of intersection of its three medians, and it divides each median into two segments, with the ratio of 2 : 1.

As G is the centroid of triangle ACE, and BE is the median, then:

`GE:BG = 2 : 1`

Given the length of BE is 15, we can use the given ratio to find the lengths of BG and GE.

Let x be the common multiplier. Therefore:

`BE=GE+BG`

`15=2x+x`

`15=3x`

`5=x`

Now that we have the value of x, we can find the lengths of BG and GE:

`BG = x = 5`

`GE = 2x = 2(5) = 10`

Therefore:

• BG = 5
• GE = 10