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, th
e 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.
2 answers:
Answer: the length of Line segment AJ is 8.75 inches
Step-by-step explanation:
The diagram of the triangle is shown in the attached photo. The two triangles formed are triangle HJK and triangle HAB. Since Line segment A B is parallel to line segment J K, it means that triangle HAB is similar to triangle HJK. Triangle HAB is smaller than triangle HJK.
Total length of side HK is side HB + side BK.
HK = 3 + 5 = 8 inches
Let x represent length of side AJ
Total length of side HJ is side HA + side x
HJ = 5.25 + x
Comparing the sides,
HA/HB = JH/HK. Therefore,
5.25/3 = (5.25 + x )/8
8×5.25 = 3(5.25 + x )
42 = 15.75 + 3x
3x = 42 - 15.75 = 26.25
x = 26.25 = 8.75
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