Question

Help needed to find BC and AC

Answer 1

See below.

Explanation:

We are asked to identify BC and AC.

Before we start, we should know that this triangle has a center called a Centroid.

What is a Centroid?

A Centroid is a point that is formed by 3 concurrent medians.

What is a Median?

A Median is a line segment that connects the vertex of a triangle to the midpoint of the opposite side.

The top part of a Median is 2/3 of the entire line segment. The bottom part of a Median is 1/3 of the entire line segment.

Using the information from above, we can identify that AB (10) is 2/3 of AC, and that BC is 1/3 of AC.

Divide 10 by
`(2)/(3)` to find AC.

`10 / ( (2)/(3) )=15 \ (AC)`

Since we know AC, we can now find BC by simply subtracting AC - AB.

`15-10=5 \ (BC)`

Therefore, AC = 15; BC = 5.

Answer 2

if we take a peek at the tickmarks on the sides, that means that the line that cuts the side is the median, so we have three medians meeting at the centroid of the triangle, bearing in mind that the centroid cuts all three medians in a 2 : 1 ratio, then we can say that line AC is being cut by it in a 2 : 1 ratio, the hell all that means? well, it means

`\cfrac{AB}{BC}=\cfrac{2}{1}\implies \cfrac{10}{BC}=\cfrac{2}{1}\implies 10=2BC\implies \cfrac{10}{2}=BC\implies \boxed{5=BC} \\\\\\ \stackrel{AB+BC}{10+5}\implies \stackrel{ AC }{\boxed{15}}`