Question

Geometry

Answer 1

Answer: UV = 52

Concept:

Additive property of length, or the segment addition postulate, states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Given information

TU = 4x

UV = 2x + 14

TV = 7x - 5

Given expression deducted from the additive property of length

TV = TU + UV

Substitute values into the expression

7x - 5 = 4x + 2x + 14

Combine like terms

7x - 5 = 6x + 14

Subtract 6x on both sides

7x - 5 - 6x = 6x + 14 - 6x

x - 5 = 14

Add 5 on both sides

x - 5 + 5 = 14 + 5

x = 19

Find UV by substituting the value of x

UV = 2x + 14 = 2 (19) + 14 = $\boxed{52}$

Hope this helps!! :)

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