Question

Find the value of the variable and GH if H is between G and I. GI=5b+1, HI=4b-5, HI=7

Answer 1

Answer:

The value of the variable 'b' is 3 and GH is 9

Step-by-step explanation:

Given:

$GI = 5b+1\\\\HI=4b-5\\ \\HI=7$

H is between G and I

Such that G - H - I

To Find:

GH = ?

Solution:

On Substituting HI we get

$4b-5=7\\\\\therefore 4b=7+5=12\\\\b=\dfrac{12}{4}=3$

Substituting 'b' in HI and GI we get

$HI=4\times 3 -5=12-5=7\\\\\therefore HI = 7$

$GI=5\times 3 +1=15+1=16\\\\\therefore GI = 16$

Now, by Line Addition Property we get

$GI=GH+HI$

Substituting 'HI' and 'GI' we get

$16=GH+7\\\\\therefore GH=16-7=9$

The value of the variable 'b' is 3 and GH is 9