Question

If EF - 3x - 11, FG = 4x-10, and EG - 28, find the values of x, EF, and FG. The drawing is not to scale.

X = 1. EF = 10. FG - 18
x - 1. EF = -8.FG = -6
X-7. EF = 10. FG - 18
x - 7. EF = 32.FG - 38

Answer 1

Part 1)
`x=7`

Part 2)
`EF=10\ units`

Part 3)
`FG=18\ units`

Explanation:

see the attached figure to better understand the problem

step 1

Find the value of x

we know that

`EG=EF+FG` ---> by addition segment postulate

we have

`EG=28\ units\\EF=3x-11\\FG=4x-10`

substitute

`28=(3x-11)+(4x-10)`

solve for x

`28=7x-21`

`7x=28+21`

`7x=491`

`x=7`

step 2

Find the value of EF

`EF=(3x-11)`

substitute the value of x

`EF=3(7)-11=10\ units`

step 3

Find the value of FG

`FG=(4x-10)`

substitute the value of x

`FG=4(7)-10=18\ units`