Question

In △FEG , point H is between points E and F, point J is between points F and G, and HJ¯¯¯¯¯∥EG¯¯¯¯¯ . EH=8 , HF=12 , and FG=30 . What is FJ ? Enter your answer in the box. FJ =

Answer 1

`FJ=18\ units`

Explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

`(FE)/(FH)=(FG)/(FJ)`

we have

`FE=HF+EH=12+8=20\ units`

`FH=HF=12\ units`

`FG=30\ units`

substitute the given values

`(20)/(12)=(30)/(FJ)`

`FJ=12(30)/20\\FJ=18\ units`