Question

If EF bisects CD, CG = 5x-1, GD = 7x-13, EF = 6x-4 and GF = 13, Find EG

Answer 1

The length of $EG$ will be 19.

Explanation

According to the below diagram, line $EF$ bisects the line $CD$ at point $G$.

That means, $CG= GD$

Given that, $CG = 5x-1$ and $GD = 7x-13$

So, we will get......

$5x-1=7x-13\\ \\ 5x-7x=-13+1\\ \\ -2x=-12\\ \\ x=\frac{-12}{-2}=6$

Also given that,  $EF= 6x-4$  and $GF= 13$

According to the diagram,  $EG= EF-GF= (6x-4)-13= 6x-17$

Now plugging the value $x=6$ in the above expression......

$EG=6(6)-17=36-17= 19$

Thus the length of $EG$ will be 19.

Answer 2

Segment EG is equal to 19