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Finding the Third Proportional to 691 and 1,066

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Solution

The third proportional to 691 and 1,066 is: 1,644.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    691 : 1,066 = 1,066 : x
  2. Step 2: Convert to fraction form
    691/1,066 = 1,066/x
  3. Step 3: Cross multiply
    691x = 1,066 × 1,066
  4. Step 4: Simplify right side
    691x = 1,136,356
  5. Step 5: Solve for x
    x = 1,136,356/691
  6. Step 6: Final answer
    x = 1,644.51

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.