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R is the midpoint of KL ;
Thus R bisects KL , which means :
[tex]KR = RL[/tex]
So :
[tex]7x - 10 = 3x + 34[/tex]
Add sides 10
[tex]7x - 10 + 10 = 3x + 34 + 10 \\ [/tex]
[tex]7x = 3x + 44[/tex]
Subtract sides 3x
[tex] - 3x + 7x = - 3x + 3x + 44[/tex]
[tex]4x = 44[/tex]
Divide sides by 4
[tex] \frac{4x}{4} = \frac{44}{4} \\ [/tex]
[tex]x = 11[/tex]
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[tex]KL = KR + RL[/tex]
[tex]KL = (7x - 10) + (3x + 34)[/tex]
[tex]KL = (7 \times 11 - 10) + (3 \times 11 + 34) \\ [/tex]
[tex]KL = (77 - 10) + (33 + 34)[/tex]
[tex]KL = (67) + (67)[/tex]
[tex]KL = 60 + 7 + 60 + 7[/tex]
[tex]KL = 60 + 60 + 7 + 7[/tex]
[tex]KL = 120 + 14[/tex]
[tex]KL = 134[/tex]
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