Answer:
The value of the variable 'b' is 3 and GH is 9
Step-by-step explanation:
Given:
[tex]GI = 5b+1\\\\HI=4b-5\\ \\HI=7[/tex]
H is between G and I
Such that G - H - I
To Find:
GH = ?
Solution:
On Substituting HI we get
[tex]4b-5=7\\\\\therefore 4b=7+5=12\\\\b=\dfrac{12}{4}=3[/tex]
Substituting 'b' in HI and GI we get
[tex]HI=4\times 3 -5=12-5=7\\\\\therefore HI = 7[/tex]
[tex]GI=5\times 3 +1=15+1=16\\\\\therefore GI = 16[/tex]
Now, by Line Addition Property we get
[tex]GI=GH+HI[/tex]
Substituting 'HI' and 'GI' we get
[tex]16=GH+7\\\\\therefore GH=16-7=9[/tex]
The value of the variable 'b' is 3 and GH is 9
