Line AB: 36 inches
Line CD: 10 inches
Line XY: Variable length

Mathematical Problem

Find the length of line segment XY such that:

m × XY = 36 inches
n × XY = 10 inches
where m, n ∈ ℤ⁺

Solution Process

XY must be a common divisor of both 36 and 10.

GCD(36, 10) = 2
Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Divisors of 10: 1, 2, 5, 10
Common divisors: 1, 2

Current Analysis

XY Length: 2 inches

Segments in AB: 18

Segments in CD: 5

✓ Valid solution: Both divisions result in whole numbers

Educational Value

This visualization helps students understand:

  • Greatest Common Divisor (GCD)
  • Factor relationships
  • Division and remainders
  • Constraint satisfaction