Answer:
[tex]\boxed {r = \frac{31}{3}}[/tex]
Step-by-step explanation:
To find the value of [tex]r[/tex], write an expression by using the following measurements of both [tex]\overline {DG}[/tex] and [tex]\overline {GM}[/tex], then you solve for [tex]r[/tex]:
[tex]\overline {DG} = r + 3[/tex]
[tex]\overline {GM} = 4r - 28[/tex]
[tex]r + 3 = 4r - 28[/tex]
Solve for [tex]r[/tex]:
[tex]r + 3 = 4r - 28[/tex]
[tex]x + 3 - 4r = 4r - 4r - 28[/tex]
[tex]-3r + 3 = -28[/tex]
[tex]-3r + 3 - 3 = -28 - 3[/tex]
[tex]-3r = -31[/tex]
[tex]\frac{-3r}{-3} = \frac{-31}{-3}[/tex]
[tex]\boxed {r = \frac{31}{3}}[/tex]
So, the value of [tex]r[/tex] is [tex]\frac{31}{3}[/tex].
