Question

1. calculate the value of x in the following diagram.

q ------y ------z
10x 50
(total length 100)

Explanation:

Step1: Analyze the segment addition

From the diagram, \( QZ = QY + YZ \). We know \( QZ = 100 \), \( QY = 10x \), and \( YZ = 50 \). So the equation is \( 10x + 50 = 100 \).

Step2: Solve for x

Subtract 50 from both sides: \( 10x = 100 - 50 \) → \( 10x = 50 \). Then divide both sides by 10: \( x = \frac{50}{10} = 5 \).

Answer:

\( x = 5 \)