Question

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.

Answer 1

Answer: the length of Line segment AJ is 8.75 inches

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