Finding the Third Proportional to 380.81 and 510.47

Step by Step Solution

1. Step 1: Write the proportion equation
   380.81 : 510.47 = 510.47 : x
2. Step 2: Convert to fraction form
   380.81/510.47 = 510.47/x
3. Step 3: Cross multiply
   380.81x = 510.47 × 510.47
4. Step 4: Simplify right side
   380.81x = 260,578.34
5. Step 5: Solve for x
   x = 260,578.34/380.81
6. Step 6: Final answer
   x = 684.27