Finding the Third Proportional to 1,166 and 1,582

Step by Step Solution

1. Step 1: Write the proportion equation
   1,166 : 1,582 = 1,582 : x
2. Step 2: Convert to fraction form
   1,166/1,582 = 1,582/x
3. Step 3: Cross multiply
   1,166x = 1,582 × 1,582
4. Step 4: Simplify right side
   1,166x = 2,502,724
5. Step 5: Solve for x
   x = 2,502,724/1,166
6. Step 6: Final answer
   x = 2,146.42