Question

Point R is the midpoint of KL. If KR = 7x - 10 and RL = 3x + 34, find KL.

Answer 1

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R is the midpoint of KL ;

Thus R bisects KL , which means :

`KR = RL`

So :

`7x - 10 = 3x + 34`

Add sides 10

`7x - 10 + 10 = 3x + 34 + 10 \\`

`7x = 3x + 44`

Subtract sides 3x

`- 3x + 7x = - 3x + 3x + 44`

`4x = 44`

Divide sides by 4

`(4x)/(4) = (44)/(4) \\`

`x = 11`

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`KL = KR + RL`

`KL = (7x - 10) + (3x + 34)`

`KL = (7 * 11 - 10) + (3 * 11 + 34) \\`

`KL = (77 - 10) + (33 + 34)`

`KL = (67) + (67)`

`KL = 60 + 7 + 60 + 7`

`KL = 60 + 60 + 7 + 7`

`KL = 120 + 14`

`KL = 134`

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