Question

Find the value of the variable and GH if H is between G and I.

GI = 5b + 2, HI = 4b – 5, HI = 3

Answer 1

Part 1) b=2

Part 2) GH=9 units

Explanation:

we know that

If H is between G and I

then

`GI=GH+HI` -----> by addition segment postulate

Solve for GH

`GH=GI-HI` -----> equation A

step 1

Find out the value of b

we have

`HI=4b-5\\HI=3`

equate the equations

`4b-5=3`

solve for b

adds 5 both sides

`4b=8`

Divide by 4 both sides

`b=2`

step 2

Find out the value of GH

`GH=GI-HI`

substitute the values

`GH=5b+2-3`

`GH=5b-1`

substitute the value of b

`GH=5(2)-1=9\ units`