Finding the Third Proportional to 10,780 and 16,565

Step by Step Solution

1. Step 1: Write the proportion equation
   10,780 : 16,565 = 16,565 : x
2. Step 2: Convert to fraction form
   10,780/16,565 = 16,565/x
3. Step 3: Cross multiply
   10,780x = 16,565 × 16,565
4. Step 4: Simplify right side
   10,780x = 274,399,225
5. Step 5: Solve for x
   x = 274,399,225/10,780
6. Step 6: Final answer
   x = 25,454.47