Question

If ef=2x-10 e f = 2 x − 10 , fg=4x-18 f g = 4 x − 18 , and eg=20 e g = 20 , find the values of x, ef, and fg

Answer 1

Look at the picture.

We have the equation:

$|EG|=|EF|+|FG|$

$(2x-10)+(4x-18)=20\\\\(2x+4x)+(-10-18)=20\\\\6x-28=20\ \ \ \ |+28\\\\6x=48\ \ \ \ |:6\\\\x=8\\\\|EF|=2(8)-10=16-10=6\\\\|FG|=4(8)-18=32-18=14$

Answer: x = 8, |EF| = 6, |FG| = 14