Finding the Third Proportional to 1,538 and 1,820

Step by Step Solution

1. Step 1: Write the proportion equation
   1,538 : 1,820 = 1,820 : x
2. Step 2: Convert to fraction form
   1,538/1,820 = 1,820/x
3. Step 3: Cross multiply
   1,538x = 1,820 × 1,820
4. Step 4: Simplify right side
   1,538x = 3,312,400
5. Step 5: Solve for x
   x = 3,312,400/1,538
6. Step 6: Final answer
   x = 2,153.71