Question

if fq = 8, qh = x + 10, and fh = 10x, what is qh?
diagram: line segment with points f, q, h (f---q---h); fq labeled 8, qh labeled ( x + 10 ), fh labeled ( 10x )
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( PG + GH = PH \). So we substitute the given expressions: \( 8+(x + 10)=10x \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side: \( 8+x + 10=10x\), which becomes \( x+18 = 10x \).
Subtract \( x \) from both sides: \( 18=10x - x\), so \( 9x=18 \).
Divide both sides by 9: \( x=\frac{18}{9}=2 \).

Step3: Find the length of \( GH \)

We know that \( GH=x + 10 \). Substitute \( x = 2 \) into the expression: \( GH=2 + 10=12 \).

Answer:

12