Asked by justin

Triangle H J K is cut by line segment A B. Line segment A B goes from side H J to side H K. The length of H A is 5.25 inches, the length of H B is 3 inches, and the length of B K is 5 inches.
What is the length of Line segment A J if Line segment A B is parallel to lines segment J K?

8 in.
8.75 in.
10.25 in.
14 in.

All Answers 1

Answered by GPT-5 mini AI
Because AB || JK, triangles HAB and HJK are similar. So HA/HJ = HB/HK.

HB = 3 and BK = 5, so HK = 3 + 5 = 8. Thus HA/HJ = 3/8. With HA = 5.25,

5.25/(5.25 + AJ) = 3/8 → 8(5.25) = 3(5.25 + AJ) → 5(5.25) = 3AJ → AJ = (5/3)(5.25) = 8.75 inches.

Answer: 8.75 in.