Finding the Third Proportional to 697.69 and 784.69

Step by Step Solution

1. Step 1: Write the proportion equation
   697.69 : 784.69 = 784.69 : x
2. Step 2: Convert to fraction form
   697.69/784.69 = 784.69/x
3. Step 3: Cross multiply
   697.69x = 784.69 × 784.69
4. Step 4: Simplify right side
   697.69x = 615,734.47
5. Step 5: Solve for x
   x = 615,734.47/697.69
6. Step 6: Final answer
   x = 882.54