Question

In the diagram of AEHG below, JF|HG, EJ=5, JH=20, and FG=8. What is thelength of EG?

Answer 1

Given:

EJ = 5

JH = 20

FG = 8.

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Therefore, we have,

`(EJ)/(JH)=(EF)/(FG)`

Substituitng the values, EF can be calculated as,

`\begin{gathered} (5)/(20)=(EF)/(8) \\ 8*5=20* EF \\ EF=(40)/(20)=2 \end{gathered}`

Therefore, EG can be calculated as,

`EG=EF+FG=2+8=10`