Finding the Third Proportional to 565 and 1,164.50

Step by Step Solution

1. Step 1: Write the proportion equation
   565 : 1,164.50 = 1,164.50 : x
2. Step 2: Convert to fraction form
   565/1,164.50 = 1,164.50/x
3. Step 3: Cross multiply
   565x = 1,164.50 × 1,164.50
4. Step 4: Simplify right side
   565x = 1,356,060.25
5. Step 5: Solve for x
   x = 1,356,060.25/565
6. Step 6: Final answer
   x = 2,400.11