Question

50 POINTS HOW DO I SOLVE THIS QUICK PLEASE

Answer 1

`\overline{JK}=33\; \rm units`

Explanation:

The given diagram shows triangle ABC, where the base AC = 55 units. Sides BC and BA are divided into 5 equal parts with lines that are parallel to base AC. This creates the smaller triangle JBK, where the sides BK and BJ are 3/5ths of sides BC and BA, respectively.

According to the Similar Triangles Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, as BK is 3/5ths of BC, then JK is 3/5ths of AC:

`\overline{JK}=(3)/(5) \cdot \overline{AC}`

`\overline{JK}=(3)/(5) \cdot 55`

`\overline{JK}=(165)/(5)`

`\overline{JK}=33`

Therefore, the length of line segment JK is 33 units.