Question

use the segment addition postulate to find the length of \\(\overline{st}\\) if \\(\overline{sr} = 2x + 7\\), \\(\overline{st} = x - 6\\) and \\(\overline{rt} = 100\\) \\(\overline{st}=\boxed{67}\\) units

Explanation:

Step1: Apply Segment Addition Postulate

By the Segment Addition Postulate, \( \overline{SR} + \overline{ST} = \overline{RT} \). Substitute the given expressions: \( (2x + 7) + (x - 6) = 100 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 3x + 1 = 100 \). Subtract 1 from both sides: \( 3x = 99 \). Divide by 3: \( x = 33 \).

Step3: Find length of \( \overline{ST} \)

Substitute \( x = 33 \) into \( \overline{ST} = x - 6 \): \( 33 - 6 = 27 \).

Answer:

27